I use kitten litter pans with a layer of litter (SoPhresh Crumbled Paper) in the bottom and layer of hay on the top. My cavies love it as they can do multiple activities there: pee & poop, munch on hay, and invariably sleep. Unless your cavies are really small, it is quite easy for them to jump over the sides without cutting a doorway. You can buy the pans online or occasionally find them in a pet store or WalMart, etc.
Don't ever fall for those corner litter pans! They are way too small and claustrophobic for a cavy. They need room to stretch out and be comfortable.