I think the 22-250 is the ultimate coyote rifle. My custom 22-250 sports a 28 " Shilen and with CFE223 powder that long barrel will push a 52 Amax at 4200 fps. Longest coyote kill so far is a little over 600 yards. Great fur bullet as well. For 22-24" barrels load the Speer 52 HP (not the match bullet, the one with the big HP) and use 34 grains of H4895. 99% of your coyotes will look like they died of old age.For that bullet to work well you have to keep velocities around 3400-3500 fps. If you want bigger go to the 25-06 or even better the 25-06 Ackley Improved and shoot the Sierra 100 MK.
I will probably have some hunters disagree with these remarks but this comes from about 800 coyotes killed with a mouth call.
I just got my latest custom rifle
back from my gunsmith. It is a 240 Weatherby with a 27" Brux. Shoots the 90 Accubond at 3450 fps and they make a ragged hole at 100 yards. I put a Viper 6x24 first focal plane scope on it. I am leaving for Montana in a few hours to hunt whitetails with my daughter in the Bozeman area.
Good luck on your coyote rifle.