You might want to try http://www.forrentbyowner.com/. You can search by your location and criteria and contact the owner directly. I'm sure you've tried Craigslist (which is always hit or miss) but you might want to try looking at some of the classified ads online for local papers like New Times or AZ Central. If you have an idea of a specific neighborhood you would like to be in, it might be in your best interest to drive through the neighborhood to see if anyone has "For Rent by Owner" signs posted in front of their house. Best of luck to you!