Ernie, As you well know I don't kill to many Pa coyotes. If'n I had to chose a caliber for out here, of the ones you listed, my first choice would be my little Sako Vixen, .223 that is what I use for "recreational" calling, second choice is my Rem 7, in 22-250, I use this rifle for those hunts we have for charity and/or bragging rights, gives me just a tad more range and knock down power. Although it is only a charity/bragging rights hunt I still like to win. Now for the money hunts, of the calibers you listed I use my Rem 700 BDL in .243. But in reality I use my Win Mdl 70 in .308 or my Rem 700SPS in 25.06. We just finished up a charity hunt last weekend - I killed nothing! It rained both days, I told my partner I have a friend from PA who visited a couple of years ago and it rained the entire time he was out here, he must be planning on coming back out! Two weeks ago we entered a money hunt and came in first.
Seeking Coyotes - I belong to three Predator clubs and am the President of one of them, we have no one, that I'm aware of that shoots a .243AI.