We have had 2 of 5 rooms OK for pets for 10 years. Have had a few problems, but not enough to make me want to change to no-dog or change policies. We charge $25 per animal, once per visit and we spend it on extra room cleaning.
In most cases problems have been dogs left alone, even just during breakfast, and often rescue dogs that haven't been acclimated. Most expensive is scratching at the door -- it took me about 3 hours to refinish one (I did not charge for it, it was a many-repeat guest with a new dog). I have one other slightly damaged I have put off fixing; I'll make a removable protective panel to hang for it when I do. The panel and the protective cover for chair and bed will be part of welcome conversation: glad you're here, what protection can we offer?
Dog owners are usually good and have paid or offered to pay when damage is obvious. We just get unusually good guests so I've not implemented a pet deposit policy.
Most useful is we say "no pets without prior approval" and almost all the time they call and showing that tiny bit of responsibility means a lot about how well the pet will behave. I'd say the best possible policy is to have a person-to-person talk about dog's behavior and needs. If dog is young, ask if it is trained, ask if it goes up on furniture, talk about what they'll do when at breakfast, observe: is it a barker, a jumper -- if so ask how they will be able to keep neighbor guests happy -- make it clear: their dog = their responsibility..