I would also suggest the 22-250 or the 243. I have no experience with the 250 but I do with the 243. If you are that good, and think you will be shooting at 400yds plus, go with the 243 and 70-85gr bullets. Coyote hunting isn't like pdog shooting, so barrel life will not be as big of an issue, but most 243's will still give 1500-2000 rounds of accurate service.
With the 243 you can push a 70gr bullet past 3600fps and that will pack a whollop on a yote still at 500yds. All that with just a hair more recoil than the 22-250.
On top of that, you'll have another deer rifle should the need arise. Load it with a suitabe deer bullet, (TSX, Partition, or the Hornady or Nosler all copper offerings) and you'll have a good 300yd deer killer as well.
Use a 75gr Vmax or, my favorite, a Sierra 85gr BTHP, and they will not move anywhere except down.