Anything that I can produce cheaply on Mars, I can produce at least as cheaply in space or on Earth without the added cost of leaving the gravity well. So we aren't going to be competing on price.
It may be possible to come up with some luxuries. For example, there may be a way to brew alcohol on Mars that takes advantage of its unique atmospheric conditions. This won't get you any drunker, but it might have a slightly different taste. The collector who has everything else might buy some. Doesn't seem like a big market though. Curios made with real Mars rock is another possibility but again, not a huge market.
Some trade in software, research, and other digital products is possible. However, there's no real reason to think that such stuff will be easier to produce on Mars. We shouldn't expect that to make up any more trade than what it does on Earth.
There may be a movie industry. Perhaps there will be a market for outdoor shots from Mars. Plentiful real estate may allow some truly realistic explosions. It's not like you can set off a real nuke on Earth, but you may be able to arrange it on Mars.
Tourism is an obvious industry, but it has its limits. Mars is far enough away that it will be an expensive trip. A thousand people a year would be a lot to go to see Mars. Perhaps some more to visit people in the colony. The movie industry might help drum up business.
Illegals are conceivable, but it would be hard to do anything really bad. Most illegal things are already available on Earth. If not available on Earth, why won't Earth mind if Mars supplies it? Particularly if it comes back to Earth. There's not a lot of cover in space to hide things nor is there heavy traffic in which to hide smuggling.
Mars might supply high security prisons. Since escapees can't survive outside without equipment, there's a certain natural security. Note that space stations would make even better prisons in some ways. However, they would need resupply by rocket ship, which would offer a chance to escape. A Mars colony can be resupplied by an atmospheric ship. That way escapees will still be stuck on Mars.
Or a low security prison colony. A group of people could walk openly around the colony but wouldn't be able to leave. It might be hard though. Prison populations tend not to be high tech. They might have trouble developing the skills to survive in Mars conditions.
An anarchists (or whatever philosophy) colony wouldn't be tradable, but it might bring colonists with their own resources. Not sure how rich anarchists are though. It's also not clear that most groups wouldn't prefer a space colony.
Overall, I think that a Martian colony will have to be generally self-sufficient. Some luxuries will move, but for the most part, Mars will have to grow its own food and manufacture its own products.