The thing about brands and reputations is that they are audience specific. Unless your country has a history of abusing tourists and investors, you do not really even need to rebrand because there is nothing wrong with your tourist and investor brands.
I'll ignore tourism because I do not really understand why you'd want drunken tourists polluting your beaches and drawing graffiti on thousand year old statues. But the process is similar to that with investors. Sell the gain, manage the threats.
For investors the gain is all about the money. If they invest in your country can they expect healthy profit? That is the primary part of your investor brand. Basically you just have to be willing to let the investors profit and investment will come. Of course you have to find some balance where the investments also benefit you but that is outside this topic.
The rest comes from all the other concerns that increase investor risk. Is there corruption? Does political instability make taxation and labor laws unpredictable? Is there unrest that might result in terrorism affecting your investment or employees? Is the government involved with things that might lead to embargoes or boycotts? Is there economic instability that might lead to things such as nationalizations?
Closer the answer to those questions is to "no", the better your brand will be.
This sounds simple but many of these issues are actually very hard problems that you cannot fake in the long run. Just saying you are committed to fighting corruption will only take you that far, you will eventually need results. Saying you are committed to peace with your neighbours is fine but you will need to actually solve all those border disputes or they will grow into real issue. While investors and politicians are usually perfectly happy to ignore human rights issues, you do not want "ignores human rights issues" as a permanent part of your brand, so you'll want some results there as well. And so on.
The short advice on this is to act in a manner that makes clear that you value your investor brand and by extension the investors and their concerns.
You can just copy the way Apple does it. Both Steve Jobs and Tim Cook have personally made clear that they personally are committed to protecting the Apple consumer brand and that Apple values its customers "more than the competition". This has been repeated over the years to the point of nausea.
Does Apple really care more about its customers? Doesn't matter, really. What does matter is that nobody can really doubt they are committed to protecting their brand with their customers. They will pay the price and the CEO will personally apologize and try to make things right. They will even fight the federal government on a case related to terrorism. Because they are committed.
That said, governments cannot generally focus on a single audience like Apple can, so you'll need to exercise some moderation and make lots of hard compromises. But whenever you make anything that is bad for investors, there should very clear and compelling reason and some person of authority should personally explain and apologize for the necessity.
Also remember that "bad" and "not what investors wanted" are entirely different things. Investors are generally fairly bad at wanting what they actually need. And knowing what they actually want. So in practice you will need to figure out what they really want and then sell it to them. You can copy this part from Steve Jobs as well.