Porta-Johns in the prison yard would work...that and a pee can in the cell, and everything's good to go.
What is OVERcrowding, anyway?!?! Until the number of inmates = the number of beds, I'd say that the prisons are underutilized. Simple crowding begins when inmates > beds. Even then, you could sleep 'em in shifts to relieve the crowding.
Chamberpots used to be the norm in society. ‘nuf said.