Honestly, it's hard to find places that accept dogs at all, let alone a dog that is one of the "restricted breeds."

If you can find a private landlord, they'll likely be more accommodating than the larger property management companies that work with dozens / hundreds of landlords. Anecdotally, I currently rent from a private landlord (she only owns this one building) and the downstairs neighbors have a pit bull. So there are definitely people who will still rent to you, it's just going to be more work to find.

Despite what is being implied by other comments on this thread, I would not recommend lying about your dog on the application. If the landlord / property management company were to find out you might find yourself getting evicted. There aren't a lot of tenant protections in RI so it's better to do things above board.