Here is one idea as to how we could implement a dark-press game on webDiplomacy.
Create a new account whose password is sent to each player. (If an organiser knows who the players are, then this organiser could set up the account and send the password by PM. If the game is really anonymous, then any player could set up the account and post the password by Global press without stating who they were. But any PM or in-game press besides this one giving out the password would be cheating.)
This account does not actually play any games (that would be multi-accounting!), it only posts to a forum thread for the dark-press game. No other account is allowed to post the forum thread; kibbitzers should be chased off (especially if we don't know who the players are), and players who post to the thread under their own names are cheating. Any player could sabotage the thread (temporarily) by changing this account's password (which would also be cheating), but then any of the players could create a new press-only account to replace it, so hopefully nobody will be such an asshole as to try that.
The biggest drawback, I think, is that the players would have to keep logging out of their real accounts and into the press account, and not mix them up; no big deal if you try to play in the press account, since it won't work and you can change, but you have to be very careful not to post to the thread with your real account, or you'll be condemned as a cheater. So it's inconvenient, and a little dangerous.
Any other ideas?