he strongest routines that I know with this gimmick involve a switch at some point. This allows the participant to examine both coins and get rid of the suspicion of a double sided coin.
I'm curious what does your routine look like in the eyes of the audience? The classic routine I know with a Copper/Silver coin is to put 2 coins in the participants hand, a copper and silver coin. The magician removes the silver coin from their fist. The magician makes a magic gesture and the silver coin turns into a copper coin. The participant then opens their hand and they are shown to be holding the silver coin.
Does that sound like the routine you are performing? If it is you could switch the coin after you have made it change. So the audience sees the silver coin turn copper, you wait a beat and pass it to the other hand (switching the coin). You then say, "If I have the copper coin you must have the silver." You can then hand them an ungimmicked copper coin and you can ditch the trick coin in your pocket. They wont see you ditch the coin because their focus is on the two normal coins.
How do you switch the coin? There are a bunch of ways. Classic ways to switch a coin include a Shuttle Pass, Bobo Switch or the Spellbound move. You can find these on You Tube but I recommend you check out Bobo's Coin Magic. You will get a bunch of switches in the book. If you like that move on to the work of David Roth and Eric Jones.
Remember with the switch, it should not look like you are switching coins suspiciously. It should only look like you are passing the coin from one hand to the other. In the audiences mind nothing happens till the moment they open their hand, by that time its too late.