If you want to stay with a factory gun go 22-250. Savage makes a 1-12 twist which you let you shoot a little heavier bullet to buck the wind. 243, 25-06 or 257 Wby are all good choices aswell. If you want to go custom the world is your oyster. 22-250 AI, 22-243 Middlested, 6.5-284, 25-06 AI, 257 STW. The only one of the last few that won’t eat you barrel as fast is probably the 6.5-284.
The guy I buy most of my stuff from does coyote depredation work in Sask. He currently uses three 22-243 middlesetds all in different twist rates and a 6.5-284. If you have the money and like fire forming, neck turning and all the other stuff that goes hand in hand with a wild cat you will be better off with a custom.