Obituaries back to 2006 can be found at Portales News-Tribune's web site.
These obituaries will be harder to find because of their age.
The University of New Mexico, http://elibrary.unm.edu/zimmerman/
has a listing of historical newspapers in their library at http://econtent.unm.edu/cdm4/results_NewMexicoNewspapers.php
I didn't read through all the entires (because the font is so small) but click on each one, read the details and you can decide which ones you want. Successful Searching!