There is a reason that most ranch houses have a 22LR bolt action rifle sitting by the door. 22LR is about as quiet as you are going to get. I have shot them without hearing protection many, many times. Good to 100-150 yds, quiet, and will kill critters with a solid hit. Or move up to a 22 Hornet, they are quieter than a 223, but they are not really quiet.
That said, I gotta agree with Hawg; what in the world possessed you to fire from under the carport?