I've been doing a lot of rulebook reading over at the Piecepack Wiki, but haven't found any cooperative games. Of course, many of the solitaire games could be played cooperatively, Cardinal's Guards leaps to mind. But are there any specifically designed to be co-ops?
Just thinking I might try my hand at creating one . . . fill in the genre gap.
To maintain the chain of succession, I would ask the winner of the last contest (Good Portsmanship) if you can take over as judge. I don't think he'll mind. Then write your rules for the contest, find a good name, and post an announcement in every piecepack-related venue you can find (this forum, the mailing list, the wiki...). Sit back and watch the entries roll in, and judge them by the deadline you state.
If you're the judge, I wouldn't enter your own new game idea except as a noncompeting entry. (In fact, that might make a good contest title for cooperative games: "Noncompeting Entries". )