Trap and shoot is the best option. You don't have the problem of potentially missing the animal's vitals and putting it through a bunch of suffering before you can finish it off, and you don't bother any body else's flock by relocation.
Since coons are so abundant, I have no moral qualms about shooting them. So many people on this site think it's somehow a sin to kill a predator...they make it almost religious. As long as the population of a predator isn't really suffering, there is no reason to sing John Lennon songs and draw rainbows while your "brother animals" slaughter your flock.
I like the way you think.