I tried adding a pet fee following Linda's solution (list the requirement and ask for money after booking). I stopped after people said they were "service animals" or "emotional support animals" and I read Airbnb's policy that not only are you not allowed to charge them a fee, but you are not allowed to ask for supporting documentation. I added something saying there would be a fee charged after the stay for excessive cleanup, and defined that as best I could, but trying to collect after a stay is generally not accepted happily by guests. So I've pretty much accepted it as one of the downsides of using Airbnb, which means more hosts will just ban pets completely.
I feel that Airbnb should allow a pet fee for non-service/ESA animals, and that they could ask for documentation ahead of time, as they do for IDs and such.. This is clearer for "service animals," but owners of "emotional support animals" must be able to provide a letter from a medical professional - not a printout from a web site offering "ESA registration" for a fee. This is a real mess (in more ways than one) as many people don't understand what a "Service animal" is and think that they can just say they have that or an ESA and it's illegal for anyone to question them. In Airbnb's case, this is effectively true.
At the very least, I'd like Airbnb to provide more accessible, clearer guidance on this issue.
Now about all the guests putting down that they are one person and showing up with more...