I would figure out what you were willing to pay for the space, and make an offer. I recently showed an apartment in a building in Chelsea where they were in fact willing to sell one of the common spaces and had already sold some other common spaces. They went for far less money than once would assume they would be worth.
If there is any history of the Coop agreeing to sell common space previously, it might be a good idea to ask around to find out if anyone knows how much it sold for - or how much they were asking. This might give you a good ballpark figure of what to offer.
Additionally, keep in mind that oftentimes the timing and the terms are equally as important as the offer itself. If you hear that there is a BIG Capital Improvement plan in the works - this might be a good time to approach the Board. They might much rather pull together the extra funds from the sale rather than raise the maintenance or do a special assessment. As for the terms, be prepared to be flexible with the close date; pay cash; or keep in mind that you could offer some kind of easement to the building - should they need to regularly need to pass through the space for regular building maintenance or the such.
Most importantly, make sure you get advise from your attorney before finalizing anything.
Good Luck! I hope you invite me to your first tiki party!