I have usually found Craigslist and Chicago Reader to have the most listings available for rent. Just FYI, the Gold Coast isn't the most "dog-friendly" neighborhood for renters either, largely in part from the number of high rises with # and weight restrictions. When dealing with more than one dog, you may want to expand your search area if at all possible.
I did run a pretty generic search on the MLS too and found about 50 listings, however your price range and BR count would obviously influence that number. I'd be happy to send you some leads if interested though. Best of luck!