I think there are two ways to answer that. First is by examining geography and history. Personally, I find that proximity and historical usage have more value than historical claims (when so-and-so discovered them). Even so, there are multiple valid claims to the island group based upon proximity, usage, and discovery. I don't see how ownership could be awarded to any one nation. It could be chopped up, but that seems like a messy option, and one which could lead to an unfortunate and dangerous military build-up.
The second solution is to decide the best and most equitable way of moving forward (which might to some extent ignore previous history, claims, and proximity in the hopes of achieving a better future outcome). I suspect this would involve placing the island group and surrounding seas under the 'ownership' of an administrative body comprised of members from all interested nations. I would think that the organization ASEAN could serve as a starting place to establish such a body (it already includes most of the nations with interest). This body could oversee competing claims and adjudicate them.
Unfortunately there is a third option. The owner will be the one with the biggest muscles, which of course in this case is China. If China wanted to they could simply claim the islands. No one in the region has the military to challenge them. I suspect, though, that China is in a bit of a dilemma. Part of them wants to exert national pride and strength and be able to simply lay claim to what they want. The other part knows that smooth flowing trade, based in part on good relations, is in their best interest. It is a delicate balance.