The Colorado Gold Rush .22 was made by Colt in 1966. Serial numbers ranged from 1CG to 1350CG and can be found on the bottom of the frame just in front of the trigger guard. The firing pin, spring and recoil cup are held in by a cross pin just in front of the top of the hammer. I have changed/installed a firing pin in a Frontier Scout just one time. As I recall it was not difficult. The main thing is to be very careful in seating the cross pin to avoid scratching the finish of the gun. Any Frontier Scout or Buntline Scout firing pin, spring, cup and pin will fit, but in your case, to make it look right, you will need the recoil cup and pin in gold plated finish. I have a wide assortment of Scout parts but I have these parts only in blue finish, not in gold. The Colt part numbers (blue finish) are: firing pin - 51716, firing pin spring - 51717, recoil cup - 51715 and recoil cup pin - 95000.
I sometimes see gold plated Scout parts for sale on eBay. Also Numrich Arms/Gun Parts Corp. may have some. You can also find a schematic for the Scout on the web somewhere. If not, I would be happy to copy one that I have and sent it to you. If the mismatched colors don't bother you, I could also send you the parts you need.
If it were mine, I would put the blue parts in and shoot the gun and hope to find the correct gold plated parts at some time in the future.