FWIW: We live in the county, couple miles from the nearest town, but are surrounded by 5 acre lots. Most everyone around here has dog, cats, and the assorted livestock running around. And coyotes.
I've seen them eating deer feed in my backyard at 1500hrs. (Stopped the feeding after seeing them). They've actually bumped against the house at around 2200hrs. Seen them crossing different roads on different days around 0900hrs. Scat in numerous places around the yard.
When the 5 month old Aussie shepard goes out, I do too. Usually with a .357, occasionally the .38.
What you choose is up to you, obviously. If a .380 works, it works; and it does. There's no need to carry a cannon if something else will do the job.