Breed a Gyarados and a Red Gyarados, wait for a day in the game, then collect your egg. Your egg will hatch to a gold Magikarp, evolve your gold Magikarp into a gold Gyarados.

Put gold Gyarados on the sixth of your list. Put a pokemon that you want to turn gold (it has to be able to evolve) on the second of your list, and a pokemon that knows fly on the top of your list. Deposit all your pokemon except the first one on your list, then enter the bug catching competition on route 15, and go to the man. He will ask if you want to leave, say no, then fly out. Your pokemon that you want to turn gold will be gold, but with gold gyarados' name.