I hunt coyotes west of the Mississippi, my three all time favorite coyote cartridge are the 20.Practical(new kid on the block), 222 Rem and a 22-204. The 20P works well with 40gr NBTs, the 222's thrive on 52gr Speer FB HPs and when calling in cat country 45gr Speer softpoints(they work well on coyotes), the 22-204 lives on 40gr NBTs it was my pelt hunting rig when coyotes were worth alot.
Yesterday Sako 222 Rem 45gr Speer
20P
22-204, ugly coyote needed to be removed from the gene-pool
I really like combo guns for called coyotes. I found some 55gr .228 softpoints for my BRNO in 22 Savage Highpower/12ga topped with a Leupold 1-4 scope has been the demise of more than a couple coyotes. I just started using a Valmet 222 Rem/12ga last year and it is a dandy. I'm headed out for a hunt, combo waterfowl and coyotes and loaded up Bismuth B's and Varmint Grenades for the Valmet it has a set of 12ga O/U barrels too so makes a nice travel rig.
The BRNO
The Valmet
Over the past couple years I've killed called coyotes with 22 WMR, 22-250, 22-250 AI, 6mm-204, 6x45, 6mm ARC, 25-204 and 6.5 Grendel. My favorite bullets for coyotes .224 52gr Speer, 6mm 55gr NBT except the ARC 75gr Speer HP, .257 75gr V-max and 6.5 the Speer 90gr HP. My shotgun load is 1 1/4 oz of NP BBs as they are in combo guns I don't have to stretch the shotgun just switch triggers and use the rifle beyond 40 yards..
I just like the 222 Rem and find it more than sufficient for called coyotes inside 200 yards and I rarely have to take longer shots than that.
What ever you pick will kill coyotes, only the 247 Herter's Ram Magnum will Kill them "deader than dead", George L. said that himself.