I've used dirty cleaning patches after swabbing the bore to patina/darken brass and steel - clean the bore with a patch after a shot, rub the dirty patch on the brass and steel. Oil the steel well, afterwards.
My old standby cleaning solution that I got from Muzzle Blasts or Muzzleloader Magazine years ago was rubbing alcohol, Murphy's oil soap and Hydrogen peroxide - I've since switched to Oil Eater and distilled water, so I don't know if this will darken brass and steel like AMH does.