Richard's right. You're basically asking how a trick is done on an open forum, which is a no-no. And quite frankly, as a working mentalist, I have several ways of performing the same "effect" -- pic dupes included -- so asking for a method is a little basic.
It is clear that you are not familiar with the standard literature out there. My advice is to take a look at it, and then begin to amass ways of doing effects that "appear" to not use any props.
It's out there, but not in a "put-the-coin-here-and-then-do-this-and-it vanishes." Mentalism is a different animal and requires a different approach. (And quite frankly, if your coin act was simply putting coins places and then they vanish, it would be a little dull. So would a mental act that just duplicated pictures. What's the context? What's the frame?)
After you've become familiar with the literature, think hard, session with friends, etc. to work out WHAT you want to accomplish, and then find a way to make that happen.
That's a very unsatisfying answer, I know. It would be great to say buy this trick or book and you too can be Derren Brown. But if you do your homework and work at it, you'll have your a-ha moment.