There are cow tags for sale in NM. Going rate is $500 -$650.
These tags are issued to private land owners by the NM Game and fish to compensate for wildlife depredation on private ranch land. Most tags will be unit wide rather than restricted to an individual ranch. To get an idea of the size of game management units you can look at unit 52 for example on the NM G&F web site. Unit 52, bordering Colorado, includes a vast portion of the Carson National Forest including the Cruces Basin Wilderness Area -no fences!
I’m happy to help with more info if you are interested.
good luck
adios
David

Just to give an update on land owner Elk Tags (actually, authorization is what NM Game and Fish calls them).
Anyway I purchased 2 cow tags yesterday 07/28/2020. So just FYI if you are still looking I believe you can find them.
good luck
adios
david

Montana has surplus cow elk tags, person needs to register on the surplus list, which is all new this year, yippee. I know ranch I hunt resides in region 5, and there is a pile of tags available for residents and NR, best to chk out Montana fwp site for info.....