Pirate Ship, Dominion Seaside
You don't lose the Coin tokens on your Pirate Ship Mat when you use them in your buy.

I think the clue is in the fact that the rules refers to them as "Coin tokens", not just "Coins".  Confusion between them and coins is understandable, but basically they're something completely different: the tokens only serve as a reminder of how many Coins you receive every time you play a Pirate Ship and choose its second option.  Coin tokens do give you Coins, but they are not Coins themselves and are not expended in the same way as Coins!