Basically, if it can kill a coyote, you can accurately shoot it, and you can afford it, that's the gun you want.
True enough
Pretty clear what I think of the .22 RF by now in this role, and the need for using an edge. I wont belabor that further.
That said, I also don't mind saying my favored farm and pest rifle is the Marlin 1894C in .357 Magnum. Good used ones can be found for under $300.
Just adequate for hunting at 100 yards, they are very accurate. They will provide more than enough power in close and they offer a fast follow up shot should one be needed. At the same time it wont carry half way across the county, should your shot go astray.
Ammo is not as cheap as the .22's, that is for sure... but you get what you pay for, IMHO. I can, however, hand load it to any level of power I want. From full out barn burner to meek "sub loads," I can do them all. With an inexpensive Lee Loader, I can span a wide power range and shoot pretty darned cheap - something no .22LR can offer. Oh yes - did I mention they can also shoot .38 Special, as well as the old .38 Long Colt and .38 S&W?
I should not forget to mention that the cartridge is a companion to my revolvers, doing versatile double duty. In rifle or handgun, it can be considered a very good caliber for 2-legged predators, as well. That is something to consider, these days, as reports of rural crime increase.
All around, I would not feel under gunned if my only "real" pest/predator control rifle beyond the .22LR, were this one.
Let it be known, too, that I'll seriously consider buying any Marlin 1894 rifle. Keep that in mind, folks