I used to hunt raccoon as a teen.
We ran walker hounds.
Yes the coon will most likely die if the shot makes it past the skin and muscle.
Just how many air rifle shots you going to hit it with before the wounded coon croaks on your neighbors back patio?
I think the .22 magnum is the perfict raccoon hunting round.
Ive seen a trapper dispatch a coon in a boxcage trap with a .22 handgun
It seems coon wont sit still for a perfict shot and with a marginal firearm?
Your chances of a anchoring single shot is not great.
If the bullet makes it through a 2x4 it should kill a coon at prudent range.
Id suggest using std velocity LR in a long barreled .22 rifle and close range on a windy night.
In town I can hear the neighbor kid shoot his air rifle.
The muffled PAP is unmistakenable.
In the house with TV going you'd mostblikely not hear it.
Usually coon once hit by a bullet coon will stop running and do some roilling around a bit trying to bite what stung it before it takes off.
Usually but not always.
Best option is
A live trap secured open a couple days as you bait coon using a can of sardines in back the trap.
Then set your trap and bait with a can sardines (poke some holes in can w ice pick) wired to floor at back the trap.
When you get your coon.
Slide trap in a big burlap bag and you can take it outta town for disposal.
How you dispatch the coon is your choice.
https://www.harborfreight.com/32-in-x-15-in-x-10-in-medium-animal-trap-63008.html?cid=paid_google|
You will need a hunting license and furbearer permit.
Just remember this.
If your trying to keep this on the down low.
89% the time the critter is not going to stick to your plan.
Its going to expire in the worst possible place, at the worst possible time, and in front of the worst possible people.
To make you look as bad as can be.
(Why do you suppose you think I said that?)