Bringing firearms into Mexico is severely restricted. Mexico allows bringing 2 sporting rifles or shotguns of an acceptable caliber and 50 rounds for each for hunting. First, a tourist permit must be obtained from the Mexican Consulate having jurisdiction over the area where the visitor resides. Mexican immigration officials will place a firearms stamp on this permit at the point of entry. A certificate of good conduct issued by the prospective hunter's local police department, proof of citizenship, a passport, five passport size photos, a hunting services agreement with the Mexican Secretary of Urban Development and Ecology (issued by the Mexican Forestry and Wildlife office), and a military permit (issued by the Military Post and valid for only 90 days) are all required to be in the hunter's possession while carrying the firearms. For additional information, contact the Mexican Embassy or Consular Office.

All firearms must be declared and registered with United States Customs on form 4457 or any other registration document available for the purpose of facilitating reentry into the United States with the same firearms.

Remember, when in a foreign country you must comply with their gun laws, and U.S. Constitutional protections do not apply.

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I hear that the gun laws are actually quite permissive if you are paying the police to help you smuggle cocaine across the border.

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Clearly through extensive licensing certain types of hunting weapons are possible to have.  

So the question is what "hunting" weapons are permitted. And how does one get the permits.

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My cousin bought some cheap ass chinese throwing stars in San Diego on his way to Mexico, and they were confiscated at the border because any type of weapon is punishable by prison time.

12020.  (a) Any person in this state who does any of the following
is punishable by imprisonment in a county jail not exceeding one year
or in the state prison:
  (1) Manufactures or causes to be manufactured, imports into the
state, keeps for sale, or offers or exposes for sale, or who gives,
lends, or possesses any cane gun or wallet gun, any undetectable
firearm, any firearm which is not immediately recognizable as a
firearm, any camouflaging firearm container, any ammunition which
contains or consists of any flechette dart, any bullet containing or
carrying an explosive agent, any ballistic knife, any multiburst
trigger activator, any nunchaku, any short-barreled shotgun, any
short-barreled rifle, any metal knuckles, any belt buckle knife, any
leaded cane, any zip gun, any shuriken, any unconventional pistol,
any lipstick case knife, any cane sword, any shobi-zue, any air gauge
knife, any writing pen knife, any metal military practice
handgrenade or metal replica handgrenade, or any instrument or weapon
of the kind commonly known as a blackjack, slungshot, billy,
sandclub, sap, or sandbag.

...
  (11) As used in this section, a "shuriken" means any instrument,
without handles, consisting of a metal plate having three or more
radiating points with one or more sharp edges and designed in the
shape of a polygon, trefoil, cross, star, diamond, or other geometric
shape for use as a weapon for throwing....

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Go to [url]http://www.mexonline.com/consulate.htm[/url], scroll down to Texas, and call the office nearest you.

I believe you are in for a disappointment.

They allow bolt-action centerfire rifles and pump shotguns up to 12 gauge IIRC, but you can bring them into the country only for a specific purpose, i.e. a hunting trip.  All the paperwork for your [url=http://www.mexonline.com/huntmex.htm]hunting trip[/url] get bundled with your firearms stuff, which consists of a special visa and a "military gun permit".  Without the hunting license I believe you cannot get a military gun permit for any firearm.

[s]People who live in Mexico[/s] Edited to say: Mexican citizens can own shotguns and .22s (no semiautos or handguns, however).  As a visitor on a short trip you can bring in centerfire ammo but it's not sold to civilians anywhere in the country.  Call the Consulate to see if people on temporary resident visas get slack.  I believe they do not.