I favor hanging a body grip necklace on the critter. You can purchase a gizzmo that fastens to the end of your staff of choice. It holds the body grip trap in place for it use. Mine is currently up at camp so can not show a pic of it. But below is one I created before I purchased the store bought one. The trick to using it is to approach the coon very slowly, and directly into it's face. When the coon gets a little more comfortable with you being there, it will stretch out it's neck to get a sniff of what you're offering. That's when you thrust this setup forward. The trap will locate itself around the neck, and an humane and bloodless dispatch will occur. As with any method of dispatch, great care should be taken. The animal will be at the far end of the chain or cable used to secure the trap. If the animal has a mind to, it can lunge forward at twice that chain length. I have a 6ft handle on my setup.
Just my 2 cents worth. We all have our favorite methods.