Oh, I get it now. I missed/skipped the first paragraph in your post that you were not hunting the coyote. Got it now.
Still I applaud it.
My deep aversion is about 10 years ago, I was riding into a big park on horseback, spotted a dead small dog off the trail. I stopped and retrieved the body; it was ugly and had been gutted by coyotes. I took the tag, buried it, and called the owner later w/the bad news. Not the hardest thing I’ve done in my life, but sad and unnecessary. Hate them.
I have set up for coyotes on our property before, no luck. Laid out nights from dusk to midnight and no joy (only a few times, not all the time!). Wish I had your success / glad you had it.