Years ago, my brother bought a Ruger M77 MkII Varmint (heavy barrel, laminated stock, 2-stage trigger). It rarely gets used, because it's a BEAST of a heavy rifle.
Later, he bought a Tikka T3 Lite Stainless in .308, and it is nothing short of amazingly accurate.
I shot my first 2 coyotes with a Marlin .22 WMR, and both ran off to die in the thick brush, and my brothers wouldn't stop giving me a hard time, so I started carrying my .30-06 (Ruger M77 MkII). My next coyote was shot with this at 30 yards. It was ugly. The exit wound was probably 6 inches in diameter.
A short time later, I bought a H&R Handi-Rifle (single shot) in .223. Not having the follow-up shot really cramped my style. I once perforated a coyote's femoral artery and blew its balls off (literally! Missed a little low) with that rifle, then my buddy rolled him with a 270-yard running shot with his .270. My brother borrowed that rifle, and shot a double with it. He called, one came in, shot it, and another came in to check out its buddy, and got shot too. Both anchored, and died within a few yards of each other.
This brother later purchased a Tikka T3 Lite Stainless left-handed rifle in .223. With his factory rifle, shooting factory ammo (probably Hornady), he had it sighted in and making tiny groups at 200 yards in about 30 minutes. The next time he shot it, he smashed a clay pigeon at 200 yards, on the first shot, while resting it on the back of a folding chair. These guns flat out shoot, and aren't picky about what you feed them.
I have seen video of coyotes running off after being hit with a .300 Win Mag. Shot placement is everything.
I have since upgraded my single shot to an AR-15. Upper is from White Oak Armament, stainless steel free-floated fluted 1:8 twist heavy BEAST, but I LIKE it! I haven't hit anything with it yet, but that's mostly because I've been focusing on other hunting pursuits. Soon...very soon...
.223 is plenty of gun for coyotes, especially if you place your shots carefully. In the coming years, reloading is going to be the only way we're able to hunt coyotes affordably, and the biggest advantage of .223 is that you can pick up spent cases off the ground (I picked up at least 100 yesterday afternoon, in a single shooting site). When was the last time you found a .22-250 case laying around? .260 Rem? .243? .25-06? .270? I've found all of these except for the .260, but usually one at a time. .223 uses far less powder (about 12 cents worth, as opposed to 25 cents). Unleaded projectiles are where it's going to hurt, but we do need to start planning for this (abhorrent) reality.
I think a .223 in a Tikka or Ruger American or AR platform will be the way to go.
