shoot it with a .22 short. I've killed many cats inside my garage using .22 short and i had no problems...same noise as a high powered air gun. But have a backup weapon handy in case the coon doesn't go down right away and comes at you. Ideal situation would be to shoot it with .22 short and have someone backing you up with a shotgun in case it charges.

Remember: COONS ARE THE PRIMARY VECTOR FOR RABIES IN MOST AREAS OF THE COUNTRY. So do not screw around with it. If push comes to shove blast it will extreme prejudice by the best means possible.