Use liver of sulfur to patina the whole piece. Rinse and dry thoroughly. Wipe off excess with a pro polish cloth, and then polish using your preferred method. Wash the piece with cold water and soap to remove any traces of dirt.
Pro Tip: Copper can dull from moisture in the air. You can choose to use a varnish on the metal if you want, but don't varnish the stone, just the copper.