Find an agent who will take that extra time to call each listing to inquire and who will push for you - but not pushy. Most properties that accept pets require a separate pet deposit - sometimes refundable and sometimes not.
The size of the dogs will also come into play. Perhaps the owner is willing to accept the dogs and the association has a size and quantity of dogs.
I like the rest of Suzanne's response below. When talking to agents, ask how many rentals they handle. Rentals don't pay agents very much for our time and gas so many agents don't want to work with renters. I have a couple agents I know who love rentals so if you need referrals let me know.