There are not many property management company's on Trulia. I suggest you Google Property management company's here in Tucson, and give one of them a call. They can help you find the rental you are looking for, based on your search criteria. This is going to be a better use of your time, allowing them to help with your search. I can recommend Genesis Property Management, have referred some clients to them. The brokers name is Dan, they do a fine job.
Best of luck to you & your search of a rental property.