Shooting coon with a shotgun is like shooting coyotes with a grenade launcher, why? No fur buyer in the country wants to buy a shotgun killed coon, most won't. And if they find out thats what your doing you'd better find someone else to take your fur to, they'll be done with ya.
If you decide to start calling coon 22 WMR is the only way to go. I've had my best success with Hornady ammo, 30gr V-max. The magic number is 2300 to 2500fps. Anymore and they won't be worth a nickel when shot, any less and they'll run right back in the tree. Look at the ft/lbs of energy compared to a 17 HMR or 22 LR, no comparison.
We also downloaded .223 ammo with 40 gr V-max's to run in the fps range above. They are awesome!!! Little entrance, no exit. They won't cycle through an AR but are great in a bolt gun or single shot. When Hornady figures out how to push a 40gr V-max to 2400 fps in a 22 magnum I'll be set.