I have never been the landlord, but since I have had pets, I wanted to weigh in.
#1--When we signed our lease, we had to give a picture of the dog and sign a Pet Addendum, stating there was a $300 non-refundable fee for the dog. This was for my roommate's dog, who is a pit bull. I think they knew it was a pit and they even said something about it jokingly. They let it slide even tho that is one of the restricted breeds. I got a puppy during the time we were there, and didn't tell them. My dog was a white German Shepherd, and, long story short, my roommate wanted to get me in trouble so she called the landlord and they came and found my dog. They said they would evict us if the dog wasn't removed. The next day, I took her to my friend's house to live. I ended up moving out and still paying my part of the rent, but, again, long story short, my roommate trashed the place, and they kept our deposit and wanted lots more money for stuff my roommate had done. Included on the letter I got was a $300 fee for the " unapproved animal." I was really pissed off and I ended up never paying a dime (way too long of a story, and its not relevant here).
#2--The next apartment I was in, they didn't care what kind of dog it was, how much it weighed, nothing. My security deposit was only like $200 and the pet fee was $250 I think, it was supposed to be nonrefundable. No additional pet rent was charged. We ended up moving out early and breaking the lease with their approval, and got a " deposit refund" check for $260. Very different than the previous story, huh?
My advice is to have a Pet Addendum, charge a non-refundable pet fee, and charge like $25/mo pet rent. Remember whatever your insurance company's rules are about breeds of pets (no GSDs, Chows, Pits, Rots, etc.). If you find an unauthorized pet, give them (curable) eviction notice, and if they don't comply, start eviction proceedings. If they do comply, keep an eye on them to make sure they stay in compliance. I wonder if there's a way to write in the addendum that they are subject to random inspection if they are found in noncompliance? I'm not sure if that's legal tho.