I like to feed the wildlife, including the coons, even though I live in town. Never had any coons dig holes in my yard. Probably because I was feeding them.
Coons will dig to find grubs under the grass. Maybe instead of trying to get rid of the coon you should treat your lawn to get rid of the grubs. Grubs don't do your lawn any good either. The coon wouldn't be digging there if there weren't any grubs to dig up. They can smell the grubs and maybe hear them under the grass too.
If you have grubs you will also eventually have gophers too, and spots in your lawn where no grass is growing because the grubs eat the grass roots and kill the grass. Those places with no grass aren't usually obvious until fall. At first they are small spots that are hardly noticeable, but those spots where the grass is dead or where there is no grass will keep getting bigger if you don't get rid of the grubs.
You probably know that grubs are worms and in the case of the ones in your grass, they're usually white, and sometimes you can see them if you pull up some of the yellow or dead grass in your lawn. Grubs will ruin a nice lawn. Turn it all into weeds and sandy spots. You'll end up having to reseed or resod. You won't likely solve the problem of animals digging in your lawn until you get rid of the grubs.
Go to Google and put "signs your lawn has grubs" in the search box, and also check out what I said about animals digging up your grass to get to them. Put "why racoons dig holes" in the search box. Get rid of the grubs and you have your problem solved before it becomes a bigger problem.
Coons can look so cute, and the big ones are pretty when they're healthy, but they can be nasty. Don't know why you would want to mess with one yourself if animal control was available to take care of it for you.