Don't mess with New Mexico. You must have a non-resident license to shoot coyotes. The 3-day license is $51.50, and the annual is $113.50. Also, once a non-resident shoots a coyote, you are not allowed to move it, skin it, or strip the tail. There is no season. There IS a season on furbearers. If you want to skin your coyote or take a fox, you need the tag which was either $200 or $300 last year. You will have guys tell you not to worry about this, but one of my friends is the Wildlife Services officer for Socorro County, and he assures me you are just asking for trouble. Very little about the NM regs make sense, just don't try to play with them. I hunt over there at least once a year on an annual license.
Good Hunting,
Bob C.