I won't repeat already good answers, so consider this only an addition to existing answers.
One thing I should point out is that if your being pressured to pass some constitution not only do you need to pass something, you need to pass something that satisfies the people pressuring you. This means you can't be too blatant in crippling the government you generate. The big trick is to sneak things into the constitution that seem innocent or that US doesn't think it can argue against, but which you know you can exploit to keep power. I'll try to mention some 'tricks' for how to phrase some of these ideas in a constitution in a way that's more likely to appear like your trying to create a real democracy while still crippling it when I can.
I'm going to mention ways to control public elections, including rather they vote for you, and ways to control the votes in the legislature body to make sure that that body votes the way you want. Most ideas could be applied in both cases, but generally it's easier to control the legislature then control public votes in general when building the constitution.
Everyone can vote, but their votes are public
This is key and important. Everyone is allowed to vote for anyone they want, but of course you will know who they voted for. Sure you can vote for someone else it's fully your right to do that. If you happen to get audited on your taxes more thoroughly, or tend to get treated harsher by the police, or are just depicted as unpatriotic slime for not supporting your great leader, well that's just a random coincidence, it doesn't stop you from voting however you please.
There are plenty of incentives, and penalties, you can enact to 'encourage' the votes you want as long as it's known who is voting for what. If people are afraid to vote against you then your find votes tend to go your way.
Your probably only get the US to approve of legislative votes being published, with the general elections expected to be anonymous. That's okay though, the small number of legislature members means it's much easier to put pressure on them to vote appropriately then it is on all the country as a whole anyways; but if you can get general elections to be public as well all the better.
Have means to remove elected legislators you don't like
If someone isn't voting the way you want getting rid of them solves the problem for you. Of course giving yourself the power to remove anyone you don't like is so blatant the US won't sign off on it, so you have to be a little sneakier.
I would suggest creating a list of 'reasonable' reasons for removal of legislators that it your confident you can 'arrange' to happen for those you dislike. The best would be making certain crimes result in an automatic removal from office which you happen to be able to help encourage someone being found guilty of.
One good option here is to say any accepting of bribes or similar is grounds for removal, then create a system that otherwise strongly encourages and allows bribery, maybe even makes it such that someone likely has to bribe others to get into office in the first place or the pay being so horrible that no one could live off of being a legislator if it wasn't for taking bribes. It could become an open secret that legislators all take bribes. However, it just so happens that only those that do things that displease you are every actually investigated and found guilty of accepting bribes.
While much harder to manage another approach is to try to get a law passed which places requirements on the legislator's extended family to meet some moral/legal/genetic/religious standards. Noone has a perfect family so if you look hard enough your find some blacksheep you can use as grounds to remove those you dislike.
One example would be to say that any immediate family caught taking bribes of receiving any benefit that could be deemed nepotism results in the legislator being removed. This is one of the few examples that seems somewhat likely to be accepted by the US, since you can claim it's an attempt to combat corrupt legislators using their family as middlemen for bribes. Again it's likely someone in the extended family would be tempted to exploit their family member's position if you look hard enough, especially if you can bait them by offering a bribe and then arresting them if they take it. if you phrase your definition of 'nepotism' generically enough you can all but guarantee the ability to remove legislators since there are always some unintentional perks to having a famous/powerful relative even if someone isn't trying to exploit them which you can claim was intentional corruption.
Have strong veto powers
If you can veto every law the congress ever passes then let them have fun bickering all they like, nothing they do will ever affect you if you don't want it to. The US probably will not accept a 100% veto power, but there is plenty of room to give a strong veto authority to yourself if necessary.
Focus on some form of Pocket Veto, that doesn't require explicit vetoing something, as it's easier to put it in the constitution without people noticing/complaining as much, and it's a little less likely to create anger in your allies if you simply fail to pass a legislation then if your blatantly veto everything.
Propaganda is your Friend, anyone that doesn't love Propaganda is a traitor to his state
Control of propaganda is a major feature of all dictatorships. if you can control the news and information that filters down to everyday citizens well enough you can convince them you are great and powerful and doing everything in their interest and that they should want to vote for you. This may all be lies, but if you can control their information enough they won't know it.
Similarly propaganda that paints dissidents and those that vote against your party lines as evil, non-patriotic, traitorous, etc will help ensure the public votes the way you want. Creating an environment where everyday citizens police other citizens into following your doctrine is great!
Finding a shared enemy to fight helps allot with this. Be it the Sunni/Shiat/whatever faiths, Communists, Illegal Immigrants, 'The West', or evil reptile men if you paint some group as out to destroy you and everyone needing to band together to defeat them your get people far more willing to go along with the party line to spite those evil whoever.
Help your friends to get elected to the legislature
Create a system where you can support the election of those you know will vote the way you want helps you to rig things in your favor. At the smallest level this could simply mean having your already well developed propaganda network telling everyone that one person should be voted for over another, if your good at propaganda, and any dictator must be, you can greatly sway votes for the ones you choose to win.
Another good option is setting up limits on how people can campaign, such as how much money they can spend on campaigning, when public speeches can be had, etc etc. The more you can regulate the ability to campaign the more you can then shift things around to favor the campaigns of those you choose to win. At minimum making it harder to campaign means that citizens have less information available to help select who to vote for and are thus more likely to listen to your propaganda, as the only available information source, for who they should vote for.
Those that vote your way get extra rewards
Create a system where you can easily reward those in the legislature body you like. You probably can't just give them money, too blatant, but you could perhaps have some sort of cabinet/advisor/figurehead roles you can allocate as you please, which happen to have good pay and require very little work, which by chance seem to always go to those who do as you ask.
Having cushy jobs for those who leave office after x years that you can give out to those who were well behaved also works well here. You can claim your just utilizing those with experience ruling to do these jobs, but if can be an unspoken fact that these are pretty much empty, or just easy, jobs provided as rewards
It's hard to vote
Make it hard to vote for everyone to lower the total number of votes and then create incentives for those you want to vote to vote for you. The more you can limit the total number of people that vote the easier it is to 'ballot stuff' votes going whatever way you want since there are fewer negative votes to counteract.
Have means to shift elections forward/backwards slightly
being able to delay elections even slightly can be a strong windfall. If populous movement is swelling against you currently just delay the vote for a month or two to give your propaganda time to settle everything. In best case get a constitution that says that your have a vote within ever 'x years' but don't specify exactly when the vote happens. When things are going your way have votes slightly more frequently (ie a few months early) then your constitution requires, say your such a good sport that your being proactive when voting. What your really doing is giving yourself some 'wiggle room' to push back votes when you need time to do some diplomatting.
You can do anything in absence of a law saying otherwise
There are all kinds of systems you can put in place that give you the right to enact 'policies' when you need to, such that you can effectively do whatever you want unless the law explicitly says otherwise. Get in as liberal a 'policy' setting scheme as possible, usually by simply 'forgetting' to list powers that you don't have, listing only powers the legislature does have, and then after the constitution is passed you simply argue you can do anything that isn't explicitly against what you said the legislature could do.
This means you can enact your own 'laws' on the fly to do anything you need, including doing things to help you keep power like creating a law tailored to getting some dissident(s) arrested, last minute gerrymandering, messing with or punishing legislatures that don't vote your way etc etc.
Encourage the legislation to not do anything
Create a system where no laws are passed and then your effectively have full power. There are lots of ways to do this. One of the simplest is to limit the amount of time they have to work, build in lots of time when your legislation isn't in office, systems that allow people to get payed for doing minimum work when in office, even trying to make it such that any vote they do make is likely to lead to someone being angry at them so that it's safer to not vote then vote.
Going along with this have a policy where it's hard to get votes passed. Maybe instead of a 50% majority you need a 2/3 majority to pass a bill. Maybe you intentionally create a system where it's absurdly easy to fillibuster and if a discussion goes too long the bill will be dismissed, or just not voted on until the next legislature meeting. This means effectively one person can stop any law being passed, get one person on your side to fillibuster anything you don't like and no laws are passed and, in the absence of laws, you get to do whatever you want.
Laws naturally expire rapidly if not voted to be renewed
If you can create a system that gives you power in the absence of laws then any law is your enemy. Letting laws naturally expire removes laws and thus expands your freedom. Having laws expire rapidly helps to clear the books of laws sooner, and thus expand your power-base. If there was a particular you really dislike that somehow got passed you only have to live with it for a little while before it expires. It also can busy your legislative body with spending much of their time simply renewing existing laws instead of creating new ones you may not like.
It's possible for the legislature to remove existing laws before they expire
This is more iffy, but having a way to remove existing laws can be another means of removing laws your unhappy with. if they manage to get one enacted wait until you can replace, or apply sufficient pressure on, those that voted for the law then encourage the legislature to vote to repeal it. Actually It's probably better to simply write the constitution in such a way that it's easy to write a new law that overwrites the existing law, but the concept is the same. You can push them to remove a law faster if you don't like the results.
Give them some actual power in areas you just don't care about
All the tricks above could work, but remember if your being pressured to do this you need to do more then just create a constitution, you need the US to accept the constitution, and you need to give enough of an appearance of it working that they don't come back and pressure you to change the constitution all over again in a year.
The best option here is to give the legislature some actual power, just make sure it's power you don't really care about. This probably means allowing them to enact minor laws that affect the every day citizens, cut which you would never bother with because they are so minor details you wouldn't have time to micromanage them.
Creating a system where they can make decisions but you can implicitly override them somehow if you really hate them helps. One idea is to say you give 'grants' for intended uses that the legislature can then choose how to divvy up and spend. So you may say that you have granted this much money to be spent on education and let them bicker and fight over what schools get the money etc, most of the time you may not care about this as it's too low level for you.
of course there is a chance that they may decide something you really hate, like all the education money should be spent to teach students how great first world countries are doing and how much your leadership sucks in comparison. If that happens you don't veto that law, but you do drop the amount you are granting for education to some trivial amount, rendering how they divvy up the money a moot point since there is nothing to spend. Then you create a new money grant to spend money on say "continuing the educational superiority over those other countries". Extensible it's a new grant, in reality it's an education grant, but with some extra verbiage in how you write it that happens to restrict it from being used in the one way you want it.
Most of the time, if you write these money grants well, and your legislature knows to keep you pleased, they will spend the grants in a way that doesn't upset you much, mostly because you don't care to micromanage how that money is spent anyways so you would have let someone make that decision it may as well be them. It will look to outsiders like your system is working great, money is being granted out and the legislature is having a very real affect on how it's spent. But you have put in a loophole that allows you to undo their decision if it ever upsets you, in a subtle enough way that you don't create the outrage that a veto would create.
The more you can actually exploit this body to all the stuff you don't want to micromanage anyways, while keeping ways to undo anything that truly upsets you, the more you can keep the US happy about your legislature without giving up anything you really want.
