Can I have separate Game Center accounts on two different iOS devices registered to the same Apple ID? Our kids each have an iPod touch and share my iTunes account.  My son now has my daughter's Game Center info on his iPod touch..  Can we get a separate Game Center ID for him?
Yes - the Game Center sign-in can be the same or different than the Apple ID entered in other places (i.e. iTunes Store and iCloud). 

Make your son an Apple ID for his Game Center and later he can use it for other uses.