Check out the restoration 101 thread in trad history and collecting forum. Seems like there's a detailed description on removing the coin. Although I think it's done in a way to salvage the coin. So there may be a quicker and easier way if the coin is junk.
I've never done it so I'm shooting from the hip here...what if you drilled a hole through the coin and then took a flat head machine screw and screwed it into the hole in the coin. It may kinda act as a press...as the screw threads into the coin, it may bottom out against the riser wood and pop it right out.
Just an idea. I'd probably follow the 101 directions though.