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An air rifle fired from inside your house, through an open window or door, at a target outside, will capture much of the noise, if the gun muzzle is inside the house. I once knew a retired Master Chief Gunner's Mate (SEAL) who kept his fruit trees free of starlings by shooting through an open window, with the air gun entirely within the house. This was in uptight, heavily-regulated Southern Calif. (El Cajon, CA).

A neighbor had a rather complete air rifle shooting gallery in his garage, when I was a kiddo. He also would practice his archery in his driveway, with the backstop and targets in the garage, at the back wall.

Stay safe.

Regards,
Dirty Bob