I never bothered to hunt coyotes in the summer, I was hunting them in northern NV in the winter, and also in ND and CO in the winter because the pelts were worth a lot more. Hand calls, recorded calls, etc. will all work when done right. A 223 is a great caliber - I used FMJ for minimum pelt damage - if you're just shooting them to shoot them like P-dogs, then use whatever you find to be accurate in your gun.
Those dogs are VERY smart, VERY wary about everything, and will bolt at the first hint of danger. Concealment, proper placement in relation to their predicted route so they'll come to you are all paramount.