Don't waste time with the 223, get a 243 Win or just use your 308 if you have one. 243 has excellent ballistics and it will take down a coyote at quite extended range.
RSAllen, your opinion is your own. You are no-ones ruler. Your advice regarding people returning to suburbia is superfluous. If all your neighbors took that advice you might have a little financial and service crisis in your neighborhood. Nobody is ever going to exterminate coyotes by shooting them. When they were originally exterminated it was with poison by the government. What shooting/killing them accomplishes is to change your status with the pack and they will modify their behavior as a result. They will keep further away from locations with people and specifically run away if a person shows themselves. That is what we want, after all ?
My work on a local sheep farm has resulted in the death of about 4 coyotes, but that small number (coyotes number over 30 which enter the property - that we know of) has resulted in them now avoiding the area that the sheep graze and anywhere near the barns. There was 1 lamb lost in the last year, compared to more than 100 lambs a few years ago.
No aggression towards predators like coyotes elevates their status until the day that they are attacking you, your livestock, domestic animals etc. Just like we see happening in urban areas (California leading the way) with ever increasing attacks on people.
I really don't care about who/what was where first, unless you can come up with a voter approved human euthanization plan for your community. If you can pull that off without your neighbors taking care of you, good luck...