I see you originally requested the information on Palm Cay. Unfortunately I don't have the condo docs handy for that condo but fairly certain that Palm Cay, 3000 Gulf Drive has a one dog limit. Condo guidelines do change so I always suggest a buyer discusses concerns with their real estate professional to ensure there are no surprises after the purchase.
There are many condos on Anna Maria Island that allow two large dogs. The condos that immediately come to mind are Palm Isle Village, La Casa Costiera, Hidden Cove, Starfish...All of which are on Anna Maria Island and in the city of Holmes Beach. Unfortunately pet restrictions are not well documented on the Multiple Listing Service so the key to your search is to find an experienced real estate professional that works the area full time. In my opinion and some will disagree, I would suggest finding a real estate professional that has an office on Anna Maria Island AND when consulting Trulia over multiple months, the real estate professional is actively selling properties on the island. There are exceptions to the rule, many real estate professionals without an office on the island do a great job but I would suggest more diligence to ensure you have a "native" real estate professional that knows condominium guidelines. The reason behind finding a "native" is the professional can ensure they are not wasting your time by showing you condominiums for sale that would not allow your two dog expectation. Good luck and I hope that helps!