In Rome, have a look at the Santa Susanna church website (English-language) for a list. A specific booking site exists at monasterystays.com.
Buyer beware: These deals should be verified by phone calls to the convent. Bear in mind that since the arrangement is informal (by hotel standards, that is), things can change unexpectedly. Forget about amenities such as AC, for example. Also, the low prices mean many places are booked many months in advance. Of course, give it a shot. Some convents can get you a room for €50. Just don’t ever think of something you can do last-minute.