Hi sjrn702 --
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.