You could set a new apple ID just for the game center for him (or you) and keep other apple-id logins the same for everything else. It seems there are some games where the gamecenter only manages leaderboard stats, etc, and others where your actual game progress seems to be tied to the id.
But on the other hand, problems will likely occur when using some games where your progress is going to sync to his device and vice-versa. This seems like a worse option to me -- imagine this for a words with friends type of game. And not sure what happens if you try to play each other.
Sort of an opinion-based question, but I guess what I would do is look into it on a game-by-game basis and find out what exactly sync through the gamecenter account for the important ones, and if there's any way to simply temporarily move off gamecenter on one device for those apps (and then eventually tie it to another account?
Or if it turns out there's only one or two apps that would be affected, one of you just bites the bullet.