Good on you. .22 long rifle placements that have worked IME have included a shot down the ear canal with the coyote broadside, a shot halfway between eye and ear with the coyote loping broadside, and some spine and lung shots that required a bit of tracking to find. The comment about a lung shot coyote going away to die where he is not problem is probably true but he might only make it to the middle of the neighbor's yard...
Even with the commercially made calls, in a populated area I'd go for soft sounds, at least at first and probably never go very loud. Dogs, neighbors etc. are a pain. One evening near dusk my grandson and I were calling raccoons in a wooded creek ravine behind his house with homes scattered along the top on both sides. We had a coon close when a homeowner across the creek from us started hollering, "Maud, do you hear that?" He started coming down the far slope through the brush with a big flashlight so my grandson and I sneaked away, stifling our giggles till we got to his house. I would have loved to hear the fellow's tale the next day as he described the wild sounds.
Coyotes have phenomenal ears. I lip squeaked a group of four from a full quarter mile away to within 8 feet. I spotted the coyotes on a rise beyond the next fence line which was a measured quarter mile away, crouched beside a fence post in the snow and called with what I had. In your case I'd give it at least 12 and maybe 20 minutes with a soft call for 10-15 seconds every minute or so, but be ready to shoot within 30 seconds of starting to call. Don't sweat it if nothing shows, but keep at it once or twice a day and from different locations if practical. You know your area and how ever you do it will be right if you kill a coyote. It is different from calling into a big canyon or across a wide sage basin.
I like calls that will fade down to a whimper or a moan and will start sound that way without requiring a big push of air and a loud blast to start. Muffle the sound into your shoulder if needed, and that's a good variation on sound anyway. There are good callers who would do it differently and give you different suggestions. A lot of different tactics will work.
Interesting project!
