Any hunters from New Mexico?

I'm headed to New Mexico next week for a few days of job-related training. I checked out the NM hunting and fishing guide and state website online, but really couldn't find anything specific about airguns. I'm really only hoping to nail a few rabbits, maybe some ground squirrels, and other small game. Am I correct in my interpretation that rabbits, ground squirrels, feral hogs, and coyote are considered non-game/pest species (requiring no license for residents to hunt with impunity)? I'd still be getting a non-resident 4 day license if I decide to bring my airgun, but can't find anything solid in what regs I can find. I think the name of the place is "Las Playas," which I think means beach...although it looks like it's in the middle of desert and nothingness? Any advice is appreciated.