As someone who has had a dog in the family for as long as I can remember; here are my thoughts on the topic, in no particular order:
1) You need to understand that a service/companion animal (even one in training) is NOT to be considered a pet and is to be exempt from any additional deposits/rent monies collected so long as the animal (and the need for it) is documented.
Now, specifically regarding PETS:
2) You need to establish a fair amount to consider as a Pet Deposit and keep it with DEPOSIT monies. Should you decide to collect "pet rent" also; you need to spell it out. Any monies collected relating to pets need to be accompanied by a lease addendum that outlines what you expect from the human residents as to how the animals are cared for as detailed below.
3) You need to set a maximum number of pets per household (2 is reasonable, with deposits/rents collected for each).
4) You need to ask for veterinary documentation detailing if the animal has been 'fixed' and had it's shots. This also indicates that the animal is under a vet's care. You also need to have a copy of the city pet license on file. This is a potential cross marketing venue for referrals that costs little to nothing.
5) You need to ask the residents to provide a picture of the animal to use in the event that the animal gets separated from the owner. Have the resident provide detailed emergency contact information to use in that event. Print 3 copies of the picture and information; place 1 in the resident file along with the pet addendum; give one to the resident; and maintain a 'pet directory' that all staff has easy access to in the event of an emergency that requires the identification of the animal. Getting this started can be an easy community service project for a young person in need of one for whatever reason. A digital camera and color printer that can do photos work for this purpose.
6) You need a clause that defines a maximum allowable size for the animal at full grown; usually in the 25-35 lb range.
7) You need a clause that outlines consequences when an animal turns on another resident or staff member. You may want to consider breed restrictions as well.
If you do not already require renter's insurance; you need to consider doing so and making sure that the insurance plans include clauses for pet caused damage.
9) If you have the 'green space' you may want to consider allowing a fenced in 'free play' area on site and posting pet cleanup stations throughout the property (these are available from Peachtree).
10) your pet addendum needs to require residents to clean up after their animals when outside the resident units and establish a small fee when they are witnessed not doing so. Alternatively, you might consider a weekly service your landscapers may be able to provide or refer you to. If you choose the latter, a pet rent to pay for this would need to be established. It also needs to address noise complaints and care for the animal while the resident is away.
11) If you do this; you need to train your staff to ask one more question when taking maintenance requests: 'If you are not at home; is there a pet that we need to know about? We do not want to accidentally let it out.'
Does this help???