Tenant asked for another dog multiple times

[Holly Moser]

We have tenants that have been with us for 6 months. The 1st time they asked for a second dog, It was 4 days after they moved in. After we told them no and we'd like more time to get to know them, they asked for a puppy again 12 days after that. Again, we said no, then they left it alone for a while, I verbally agree to reconsider a dog after they fixed damage they did to the walls while moving in. They referred the damage back to us because there are no doorstops in the home. Immediately, red flags and we decided against the dog because of their lack of ownership. In that two day window between the verbal agreement and the denial or request, theg decided to put a deposit down on a puppy. The female tenant just told me today that she registered their current dog and the new puppy as emotional support animals. 

What requirement do I have to allow a new puppy in our newly remodeled home? Or does anyone have any FHA laws or resources I can refer back to?