I live in a rural lake subdivision. My dog likes to be let out in the middle of the night & last night I let her out at about 1:30 am. She usually runs around the yard (e-collar) and goes to the bathroom and five minutes later I let her in. Last night as I am walking up to the sliding glass door to open it and let her in she is sprinting towards me as I am opening it up & a coyote is 10 feet behind her and 20 feet to the west of me. She damn near was killed, drug off & eaten. I tested my Moultrie M-880c in my yard before using it & you can see it looks more like a neighborhood than rural property. I might declare war. (I removed the fence.)
You got the makings of a first class decoy dog. Look up decoy dogs for coyote hunting. Unless you have a foo foo dog or cat I wouldn't worry about your dog and coyotes. But if it gives you an excuse to shoot in the area I'm all for it. I have them come in by my kennels quite often.