N.M. Stat. § 14-11-12
All legal process against nonresidents, unknown or absent parties, notices of sale of real estate under foreclosure of mortgages or executions, trespass warnings and other documents, the publication of which is required by law to be made by posting written or printed notices in public places, may be published instead of being pasted up, in English and Spanish, in some newspaper published in the county, if there be one, if not, then in some newspaper published in some other county of the state for the same length of time it may be required to be posted, and when so published it shall not be necessary to post such notices in public places: provided, that the person who may have to pay for such publication shall have the right to designate the newspaper in which the same may be published: and provided, further, that no newspaper shall be allowed to charge more than the price fixed by law to be charged for legal advertisements.
NMS § 14-11-12