Picking colors for an abstract game (game design)
If it's only for two players, you're in luck. Chess and Go are both over a thousand years old, and both use the classic combination of Black and White.

If you insist on having a colour, though, you want to follow black and white's example; have lots of contrast between them, and keep in mind accessibility. Amy's preference for red and green is far less important than Bill's colour-blindness when it comes to designing your game. Any dark colour and white will do this job, and this is commonly seen in chess sets; Red and White is common.