Number one rule for coyote behavior: If there is food, there will be coyotes.

If there are coyotes now, and more importantly, sustenance for coyotes, even if you run those dogs off, new ones will show up sooner or later, OR they'll simply get better at not letting you see them. To combat that, you'll need to keep up a staunch defense against them (keep throwing lead at them every chance you get). Or you can get pro-active and scout your land to find their den-sites, find den sites, and make an effort to disturb them (doesn't take much), if they can't feel secure in their hunting areas, they'll distance themselves.

Keep in mind that coyotes have broad home ranges (up to 10mi radius in certain areas or times of year), and they're very mobile during most of the year. Coyotes can use up to 200 different dens in a year, rarely spending more than a week in one den, depending upon time of year, pup mobility, food resources, disturbance pressure, etc etc. So if you find one hole, don't stop there.