As others have said, the landlord has the final say, and good references certainly help. A property management company recently told me that they aren't particularly concerned with an overall low credit score. They look for broken leases, evictions, late rent.
Lease property is pretty limited right now, but I am happy to help you locate rental property. We can set up an automatic email that comes to you as soon as a property is listed on the MLS.
Please contact me here or call me directly at (512) 635-2117.