Aww. Shoot. I have a soft spot in my heart for coyotes, but I do understand that they can cause problems. Good luck man.
Yeah. Dumping it on the other side of the woods wouldn't do any good, because it'd just find its way back no problem. Usually when they're trapped and removed, they're relocated to a forest preserve or something. We have coyotes around here in the city and surrounding suburbs, but they don't cause too many problems. Every now and again the sheriff/police/park rangers will put out notices reminding us to keep lids on our trash, stay with our pets when we let them out at night, not interact with them, etc. I think it tends to work, cause I watch the local news almost every morning, and I don't think I've ever seen a report about an aggressive coyote encounter. If we had one, they'd probably jump all over that, cause they report on some of the most inane stuff.