They've got a power and force that you've never seen before

[Wisemon]

That wasn't the coin itself; that was the imprint left by years of the coin being in the morpher. Alpha said in the episode that the coins were destroyed, which is why he advised Adam not to morph. The coin might've been in his belt buckle in costume, but that's a failing at the Japanese end. Oh, and the ninja coins and the dino coins were the same coins. They'd have to be. I didn't see them getting new ones in Ninja Quest or the movie.