I'm tempted to say "have them play poker", except it uses lots of domain-specific knowledge as well as general rationality. Perhaps if you could generate random games from a large enough space that people don't build up game-specific skills, and the games just end up testing general rationality? While poker-like games don't test all aspects of rationality, there are some things like "ability to keep making good decisions when frustrated / bored / angry" that these games test very well.

I think people would develop skill at the whole class of games...but at the same time, they would be improving their rationality.