Spitzmaus
Your persimmons aren't ripe. Here's a technique that will let you make certain they're fully ripe before you need them. Wrap each one in two layers of plastic wrap. The reason is to minimize exposure to oxygen, so they need to be well-wrapped and fully enclosed. Put them into a warm place - 100¡ to 115¡F - for 24 hours. They'll either be fully ripe or very close. If you want to be dead certain, 48 hours will do it.
The persimmons will still be firm to the touch, but that astringency will be gone. They grow wild around here, and I hate that water-balloon texture they get after the frosts. So I pick them in late October and do the wrap and heat technique. It works most wonderfully. If they still have any tinge of green on them, I leave them for another 24 hours to be absolutely sure. My warm place is a heating pad under a cardboard box with some towels draped over top.
The technique is a parallel to what's done in Japan. They put the unripe fruit into empty sake barrels. The alcohol evaporating from the walls drives the air out of the barrels, so the fruit ripens. Since I don't happen to have any such barrels, I do it with plastic wrap.
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