My SO and I rent an apartment in an owner-occupied building. The owner's daughter had a dog in our unit before we moved in, but our first year we weren't allowed to have pets. When negotiating our next lease, we asked and he said we could have one dog. He didn't include any restrictions on breed or weight, which we really appreciated. (The owner had two dogs himself, so he was clearly dog people.) His only ask was that we clean up the yard in a timely fashion. No pet deposit or extra monthly fee. We know we're really lucky.
And as it turns out, our dog refuses to use the backyard as a bathroom, so we take him on lots of daily walks (always cleaning up after him). As a teething puppy he did chew on molding some and pull up some carpet loops. The carpet is really, really old, so I don't feel too bad about it, but it's a fact. (We got a large outdoor rug and covered as much of it as we could until he grew out of that phase.)
My SO and I have talked about being landlords and would really want to rent a pet-friendly place if so, assuming of course that we get to meet the pets beforehand. We know what an upward hill we'd face in finding another rental for our sweet 90 lb dog, even though he doesn't shed. I think you'd get lots of grateful tenants if you vet them carefully before signing the lease.