Prepare for disposal before shooting coyotes is good advice.
If you’re going in for that much labor, might as well look into putting up fencing that will keep the coyotes out.
Yes, it can be expensive. But so can losing calves, lambs, chickens, and well-trained hunting dogs, as well as the emotionally draining prospect of continuous warfare with a damned wild canid.
Maybe it will take awhile due to the expense, but even doing it in stages is better than doing nothing, since you know eventually it will be complete and you won’t have to worry so much.
We fenced to keep our hunting dogs inside our property. Since creating a palisade was not our priority, we put up a 6’ metal fence that looks like black spears with arrowhead points at the top.
Everyone told us it wouldn’t keep deer and coyotes out, but it does! In fact, because coyotes can’t or won’t get inside, we’ve had wild rabbits set up housekeeping in a juniper-covered embankment. They come out at night to graze.
Your coyotes must not be particularly motivated because of good eating outside the fence. I knew a woman with an 8’ block wall, who was working in her backyard when a coyote made it over her wall, snatched her small dog, and with a running leap hurled back over.
Add to that the price of fencing 7 acres, and bullets are a whole lot cheaper.