Shooter you say that it's a never ending process and if you kill coyotes off a property new ones will just replace them every year so you need to be on a trapping program. Let's say you have 15 yotes on a property and kill them all theorhetically couldn't 15 new yotes replace them next year? Hence the need for trapping every year. Why not just not start the process of killing them and just deal with the original 15. I've just got the impression from what you've said that you will never be able to eliminate the yote problem, so why waste money on trapping if they're just gonna be replaced by next year?
Now this is just my opinion on this so take it for what it's worth. It is a constant fight but you target your fight so it does the most good. You target the coyotes prior and during fawning season. This way you increase fawn survival and run traps when it is a bit cooler. You shoot coyotes you see during the rest of the year then start over.