Conway Greene Co. has an online database of NMSA 1978 here:
http://www.conwaygreene.com/nmsu/lpext.dll?f=templates&fn=main-h.htm&2.0

This database is current through the first session of the Forty-Ninth Legislature (2009)

THOU SHALL NOT CARRY

• Liquor establishments – except by a person carrying a concealed handgun who is in possession of a valid concealed handgun license for that gun pursuant to the Concealed Handgun Carry Act; provided that the licensed establishment does not sell alcoholic beverages for consumption on the premises (30-7-3 NMSA 1978; 4th degree felony)
• Schools – except by a person older than nineteen years of age on school premises in a private automobile or other private means of conveyance. (30-7-2.1 NMSA 1978; 4th degree felony)
• University premises – except by a person older than nineteen years of age on school premises in a private automobile or other private means of conveyance. (30-7-2.4 NMSA 1978; petty misdemeanor)
• Preschools – (29-19-8 NMSA 1978)
• Courts - unless authorized by the presiding judicial officer for that courthouse or court facility. (29-19-11 NMSA 1978)
• Tribal Land - unless authorized by the governing body of an Indian nation, tribe or pueblo. (29-19-10 NMSA 1978)
• Public buses – (30-7-13 NMSA 1978; misdemeanor)
• Airport Security Zones
• State Parks – except during designated hunting seasons or in authorized areas. (19-5-2-20 NMAC)
• Most Federal Properties – (Refer to the U.S. Department of Interior rules and regulations relating to firearms possession on federal properties)
• Private property – where the owner has posted signs indicating that you may not carry or if the owner tells you that you cannot
• While under the influence of alcohol or drugs – (30-7-4 NMSA 1978; petty misdemeanor)

Be very aware of these. Once you get used to carrying a concealed handgun, you tend to not think about it as you go about your daily life. It will be very easy to forget as you go to Pizza Hut or to pick up your child at school.

The New Mexico Concealed Carry Handgun Act of 2003 specifies the following "applicant qualifications"

A. The department shall issue a concealed handgun license to an applicant who:

1. is a citizen of the United States;
2. is a resident of New Mexico or is a member of the armed forces whose permanent duty station is located in New Mexico or is a dependent of such a member;
3. is twenty-one years of age or older;
4. is not a fugitive from justice;
5. has not been convicted of a felony in New Mexico or any other state or pursuant to the laws of the United States or any other jurisdiction;
6. is not currently under indictment for a felony criminal offense in New Mexico or any other state or pursuant to the laws of the United States or any other jurisdiction;
7. is not otherwise prohibited by federal law or the law of any other jurisdiction from purchasing or possessing a firearm;
8. has not been adjudicated mentally incompetent or committed to a mental institution;
9. is not addicted to alcohol or controlled substances; and
10. has satisfactorily completed a firearms training course approved by the department for the category and the largest caliber of handgun that the applicant wants to be licensed to carry as a concealed handgun.

B. The department shall deny a concealed handgun license to an applicant who has:

1. received a conditional discharge, a diversion or a deferment or has been convicted of, pled guilty to or entered a plea of nolo contendere to a misdemeanor offense involving a crime of violence within ten years immediately preceding the application;
2. been convicted of a misdemeanor offense involving driving while under the influence of intoxicating liquor or drugs within five years immediately preceding the application for a concealed handgun license;
3. been convicted of a misdemeanor offense involving the possession or abuse of a controlled substance within ten years immediately preceding the application; or
4. been convicted of a misdemeanor offense involving assault, battery or battery against a household member.

For more information, please click the link below to download the entire text of the New Mexico Concealed Carry Handgun Act of 2003.

The State of New Mexico says the following regarding the "Unlawful carrying of a deadly weapon"

NMSA 1978 Chapter 30, Article 7, Section 2 (Abbreviated)

A.  Unlawful carrying of a deadly weapon consists of carrying a concealed loaded firearm or any other type of deadly weapon anywhere, except in the following cases:

1. in the person's residence or on real property belonging to him as owner, lessee, tenant or licensee
2. in a private automobile or other private means of conveyance, for lawful protection of the person's or another's person or property