Usually the MLS listings have some information about pet policies ... Please call me - I will be happy to show you where to look for that information. It states if the owner allows only certain types of pets (cats only, or dogs only), how much pet deposit, whether it is refundable or not, etc.
A couple things:
First, when doing a search on Trulia, click on "More Filters." A little bit down you will see the pet options check boxes. So use that when you do your search.
Second, in general, homes rentals are accommodating to pets -- for a price. Expect to have to pay a pet fee for the privilege.
If you're having any difficulties finding as place, give me a call at 623-203-2250. You just tell me what you're looking for and I can do all the work.