Make it Arimaa
. It's a game explicitly designed to be more difficult for AIs than it is for humans.
yeah "go" is for example one of the more known ones that is hard for computers. but also, while possibility of bots does eliminate some of the games immediately, it isn't a huge problem but a thing to keep in mind.
if its a custom and complexish game, with partial information or such, it becomes increasingly difficult to write a human competitive ai for it, and people capable of doing so pby have better ways of earning money. and this is combined with site owners actively banning bots.