I raised horses for years and would kill 12-15 every year as my mares were giving birth. They still walk the fence line staying on the neighbor's property. Got one 2 weeks ago with a STI 10mm 2011. He was young and was trying for one of my barn cats. Got him with Underwood Ammunition 10mm Auto 155 Grain XTP Jacketed Hollow Point Muzzle Velocity: 1500 fps. Went in between the shoulder blades and came out in his chest. I have used .22's to .45-70 just make sure of shot placement.
I've used a 25.06 for many years for varmint control. I have never shot a better round for it! Has great range and Ive never had a coyote or ground hog move after being hit. .223 will work just fine also.
.22LR will take down the coyote. Question though, are you in town or in the country? What is your backdrop? What could you hit of your neighbors? own? passing vehicles?
Some rounds are just better suited for one type of action and some are more necessary in other types of action.
I would suggest a round you are comfortable shooting, already possess, and not overkill for your situation. If you are on a small property with close neighbors you will want to take your weapon of choice into account.
Also, are you sure what is taking your chickens? I've lost most of mine to opportunistic opposums and stray dogs than anything else. In that order.
we go back several thousand feet and at the rear of our property is an abandoned rail way bed which is what I believe the predators use to travel in on. So colleteral damage is not a concern no homes or road ways in the vacinity
I took one several years ago with a 4" barreled .357magnum revolver.
I was hunting deer, but the opportunity arose, and I had a resident hunting license in my pocket, sooo...
Ran in circles (in place) about 3 times, then dropped. 60 yards was not enough distance for the coyote.
If you're not interested in saving the pelts, just about anything will work. A .223 would work just fine, I would use it. Heck, the next time I'd pick up the .243 just for a change of pace. The next time a .270, then maybe the .30-06, or the .300 win mag, the M1A .308, a .300 ultra mag, .338 win mag, even my .50 cal muzzleloader. I don't want any of my pets to feel left out of the fun.
Seriously, I just started coyote hunting last year, but have yet to shoot one. Last year I was hunting with a Remington 700 in .243. This year I'm going with the .223.