I have a house I'm trying to sell in town out on the lake (north-side), and a couple of pieces of lake view property on the south-side.
I never hunted south of Tucumcari, and except for a couple of informal winner takes all contests didn't call (nobody did), but I've killed more there in a day just shooting "targets of opportunity" while driving to friend's places, than I've gotten here hunting them.
You'll have to get permission to even get on to lots of places, much less hunt (it's almost 100% private land), but try north of Logan on the Strebeck, Trigg, McCarty, and Libby spreads. If every man woman and child from Logan, Mosquero, Nara Visa, Armistad, and Roy was calling every day, it still wouldn't be a high pressure area, too much land and not enough people.
North of Steve Trigg's up to Roy and east of the Bell is a good area too, but the ranches are smaller so you'd need a lot of permissions. Unless they've changed ownership you won't get permission to hunt the Bell Ranch (couldn't even get it to follow a livestock killing cat), but just north of it in the river valley around Sabinoso there is (a little) public land that should be excellent.
You're in a great area for coyotes for sure.