I meant for my first post to be puppy related but more on that later. A few coyote stories to share.
One morning I let two full grown labs out of the front door to air out before feeding. As I called the dogs back to the front door I could see them being chased from the dark into the light of the front porch by a pair of coyotes. The coyotes turned off as i stepped into the door way at about 20 yards away. Sobering stuff.
A neighbor shot a coyote within a year of that event as it was coming up to his sliding glass window looking at his young son and his smaller bodied yellow lab that were in the house. He said once he saw the coyotes nose on his glass window that it was time for this one to go.
15 years ago I had a coyote false charge an Alpha female black lab of mine. Twice the coyote made an aggressive move towards my lab before planting its front feet as my dog went in the other direction. This was the only canine that lab ever backed away from. It took a voice command to move the coyote back. This was the only time I ever had a coyote hesitate to run off once I was confident that it had seen me. I realized later that it must have had pups nearby.
Another close call involved walking a black lab pup that was under six months old off leash in a field and a group of coyotes tried to engage it in play. I ran toward the three coyotes as I have heard they lure in young dogs before attack. The coyotes were gone in a flash at the first sight of me. The whole incident lasted less than 30 seconds.
The last close call involved a walk in the woods with a three month old puppy. When we made it back to my friends cabin a neighbor called to report that a coyote followed behind us for about 100 yards on our path. I never noticed the coyote myself in this incident.
It would seem puppies and smaller bodied dogs are most at risk.
As for weapon choice I would say hunt them like deer from a blind and get a .243 rifle with a fine scope. I would not bring the dog along for this hunt. As noted by others the chance of an accurate shot at a moving coyote or injury to your dog dictates great care if using your gun on the coyote during a typical day afield with your dog.