Andrew, the 22-250 works but if its windy and your going past 300 yards I would look hard at the 6mm on up. I really like the 25-06. I don't know what ammo is available around you or how easy it is getting reloading supplies so you should take that in consideration of what caliber. The Winchester 243 is hard to beat for availability, differant bullet weights and cutting the wind ability. Other calibers you might consider would be 257 Weatherby Magnum, 6-06, 6.5 x 284, 270 WSM and 7mm Rem Mag.
If your already comfortable with the 270 Winchester you can always load it with 90-110 grain varmint bullets or a good hot load of 130 grain bullets. The 270 has been around a long time for good reasons. You start looking at the ballistics and it doesn't take much of a back seat to the long range calibers. Ammo can be found every where and its not very expensive.
I can't imagine you would be shooting coyotes that were in amongst the herd unless they were trying to take down a calf.
If your already comfortable with the 270 Winchester you can always load it with 90-110 grain varmint bullets or a good hot load of 130 grain bullets. The 270 has been around a long time for good reasons. You start looking at the ballistics and it doesn't take much of a back seat to the long range calibers. Ammo can be found every where and its not very expensive.
I can't imagine you would be shooting coyotes that were in amongst the herd unless they were trying to take down a calf.