Unfortunately, THE PIRATE QUEEN is closing from lack of ticket sales -- no one is going to see it, and not because hords of people are clamoring the Hilton Theatre, thus wiping out their inventory on EVERYTHING.
Playbills are printed en masse, so they never run out. Boxes and boxes of them will still be around way after the show has closed. So much so, that if you stop by the theatre after the show's closing, they might even give you a box full of Playbills. A friend did this when SIDE SHOW and DANCE OF THE VAMPIRES closed, and the box office personnel gave him a box full of Playbills.
Merchandise for THE PIRATE QUEEN will soon be discounted, so don't worry about any selling out. Non-theatre people don't care for merchandise of shows no longer running, so all the NY souvenir stores will have their THE PIRATE QUEEN merchandise discounted in a few weeks, so I'd wait. The reality of having to clear-out non-sellable merchandise prompts them to do this. This happnes to EVERY show that closed quickly. It's not a first.
Here is a link to a site which always has closed shows merchandise quickly discounted (AFTER the show has closed):
http://www.broadwaynewyork.com/search.aspx?keywords=Pirate%20Queen For those out of the USA, though they do not list the souvenir program book, I would contact them directly, either at the phone number or email, and state you are interested in purchasing it. I'm sure they will help you out.