I wouldn't do this as a game but is a cute idea to have babies in ice cubes lol Baby shower game ~ "my water broke" ~ put a frozen baby in your drink and when your baby is unfrozen, yell "my water broke". first one to yell wins!
Games - Bottle Chugging I don't know if this is the crowd for this, but sounds fun to me. Fill baby bottles with your drink of choice. Make it a bit more fun for non-pregnant guests by adding some booze, then have guests race to chug them down.