I found the cartridge I would use when hunting Coyotes depended on the area and the prevailing conditions at the time.
I was hunting coyotes for several Dairy Farms, Feed Lots, Ranches, and some small farms.
Conditions varied from river bottoms to higher mountain valleys.
The river bottom hunts were the most tedious, and shots were seldom over 200 yards, so I used the 223rem or 22-250.
Around the feed lots, I used a 22 Hornet with 35 grain hollow point bullets, which were pulled from 22 WMR cartridges. They were called "Speer TNT" and I had a tough time sourcing the bullets in that weight for reloading, other than from loaded cartridges.
I needed a bullet that expanded explosively, but wouldn't exit and ricochet, or heaven forbid, hit a commercial animal.
For the high "plateau" areas, where there were several ranches and Dairy Farms, shots could be as far out as 400 yards, which isn't difficult, other than mirage, howling cross winds, and bright sunlight reflecting from snow, etc.
One of the problems I ran into, especially during calving time, there was often an audience. Missing wasn't an option.
One hunt I was on, the wind had torn the roofs off several hay sheds, barns, and houses the day before. It was still blowing, but with much less intensity, with spells of calm.
Coyotes don't like wind much and only venture out in it if they have to, for food, or they're chased out by something. They hug every bit of cover and protection available, such as ditches, ravines, willow brush, fence lines where the vegetation has grown, whatever.
I was using a 223 rem when I first started hunting those conditions and set up a target at 400 yds to see how much wind would deflect the bullet. There was about a foot of snow, so impacts were quite visible with a spotting scope. Slogging through a foot of hard crust snow, is not a pleasurable experience, no matter how young and fit you are.
25km Wind drift on a 55 grain 223 cal bullet at 400 yards at 3200 ft elevation was right around 5 feet. To much to figure in "Kentucky Windage" holds for consistent hits.
I tried a 243 with 65gr Vmax, but there was still more drift than I was comfortable with.
Next on the list was a lovely Voere 308Win, which shot flat base 150grain, fmj bullets very well. It worked very well, cut the deflection from the wind down to 5 clicks on my scope's windage turret for a 400 yd shot, in 20km wind. The only issue, those fmj bullet just kept right on going, and this rifle didn't like light, explosive bullets.
I finally settled on four different rifles to cover the conditions I was hunting. This wasn't as tedious or confusing as it sounds.
I knew the day before which area I would be hunting, and the conditions likely to be presented.
My Coyote battery included 22Hornet, 22-250, 260 Rem on a 700 Remington, with a factory Varmint barrel, with 95 grain Vmax, for hunting from hay sheds and off the tops of hay stacks, Tikka T3 Lite, with 95 grain Vmax, for walking the covered areas hunts.
If you are hunting different conditions, you need different rifles/cartridges.