You can try property management companies such as http://www.ammre.com or search through Craigslist for rentals.
Syan Real Estate
Call/Text: (505) 730-8181
FREE Listing Alerts: http://www.syan.com/alerts
You can try an apartment locator service or property management firm who can worry about all the searching for you, and once they find something that meets your criteria, they can set up a showing for you when convenient. Our company All Quadrants Management is one of the companies in Albuquerque and Rio Rancho that can help you out. Good Luck on your search. http://www.aqmabq.com