[Tainan]

My vote is to go traditional:
.220 Swift - a tried and true solution. I was weaned on this for ground hogs out to about 200 yards.
22-250 - works like a charm but its a 'hotter' round which may effect barrel life.
.223 - shoots the same round and ammo is cheap and easy to find. Good bolt actions are affordable. Flat shooting out to about 250 yrds or so. POI is POA out to about 200 or so.

Any of these are good for what you want. Ammo cost might be the deciding factor all things considered.
Good shootin' !

[yarddog]

If I were going to spend the rest of my life hunting Coyotes and could choose any gun ammo scope etc. withing reason it would be:

A Colt AR-15 H-BAR with a 3X9 Leupold or even a 4X Leupold. I would shoot commercial .223 55 grain hollow point boat tails.

I could get by just fine with a rifle I once had. It was an H&R Handi-gun in .357 maximum. It was a break barrel single shot and I was not expecting it to be accurate but it turned out to be a great shooter, more accurate than most of my bolt actions. That .357 Maximum with a 158 grain jhp out of the 22 inch barrel was hot, quite a bit hotter than a 30-30. Than main thing is it was light and carried like a dream.

Another possibility would be one of the HK .22 magnum auto loaders. They are probably getting hard to find but were uncommonly accurate.