There are folks who can duplicate the original parkerized finish (which wasn't greenish, by the way), but if you shoot it a lot there isn't much point in spending extra dollars to make it look new, only to wear it out again. Bill Adair and Doug Turnbull are noted firearm finish restorers. Otherwise, pretty much any decent gunsmith can offer a simple reparkerizing job that will look close and be functional.
If I'm not mistaken the finish sometimes turned a greenish hue after storage in cosmolene grease. Originally Remington Rands were a sandblasted Du-Lite blue finish, then later a dark grey parkerizing, then the last guns were finished a more light grey color.
BTW I used to have a Remington Rand with an original finish that was a different color on each side of the frame.