Both Pat Esterly and Nancy Anderson let me know about this link.
The New Mexico Death Index Project has a new web address: http://www.usgwarchives.org/nm/deaths.htm.
This private project is a database of nearly 51,000 names of people who died in New Mexico between the years of 1899-1949. Sam Quito Padilla Gonzales, a member of NMGS, headed up this project. The site is hosted by USGenWeb.
The site includes instructions on how to access death certificates listed in this database.
Link to the New Mexico Death Index Project.
Link to Instructions on How to Access NM Death Certificates.