M.M.
We had to give a dog up for similar reasons. He couldn't control his peeing and would go everywhere.
I found a farm, they keep him outside and he is happy, 5 kids, another dog, several cats. I felt horrible because I felt that I had failed, but I didn't.
I gave him what he needed, a new lease on life and a place where he was not yelled at constantly.
So put an ad in the paper for a farm, say outside barn cats. When people call, let them know what you are dealing with. Ask for something, even just $10 a piece, that way you know they are not being taken by someone who will bring them to an animal testing facility for money.
Good luck. I am a cat person so this would be very difficult for me. I even had a lot of tears letting Onyx, the peeing dog, go.