Consider using subsonic .22s, it will make it about as quiet as a pellet gun.
If you are using a semi automatic, the action of the bolt and the bullets hitting the target will be the majority of what you are hearing.
If you want to go quieter, get a bolt action .22 with a threaded barrel and shoot subsonic long rifles out of it. You will hear the click of the firing pin being struck and the impact of bullet on target.
I know this because with subsonic .22s I can hear the hammer fall on my Henry .22 and the impact on the target. If this were any quieter it would be about as quiet as an air rifle.