Sadly, New Mexico did not require the recording of births until about 1919, so you would only find a state birth record if he applied for a delayed birth certificate-which was done by folks born without one later in life. However, if the state already told you they had no record, chances are there isn't one, but you might make the request again, and specify "delayed birth record"-may make a difference.


Some counties did record early births on their own-you might contact the county clerk and see if San Juan county did this.
http://www.co.san-juan.nm.us/Dpt/Clerk/_Default.asp

His application for a social security number should also have his parents names-that can be obtained from the SS admin.
or perhaps an APPLICATION for a marriage license-not the license itself. If by chance he was in the military that's another option for records.