New Mexico Varmints
I,ve hunted NM the last two years for big game with good success, also killed a few predators.
As a big game license holder you do not need another license for predators.
I believe that as long as you are hunting coyote and foxes you don't need any license, only if you want to shoot a bobcat.
Coyotes are abundant in that state, I would concentrate on the east side of the state between Clovis and Hobbs and west towards Roswell. The terrain is ideal for calling and it is a target rich environment. Good luck