There's a site that you can play mafia on, I forgot it's name. Getting a game of mafia going on the forums would be a bitch because half of it would need to be through pm's.
You're thinking of Epicmafia.
It probably wouldn't be
too bad. Of course, it wouldn't actually run within the same timeframe as a normal mafia game, and PMs would be used extensively, but
it can be done.
At the start of the game, the game master (presumably me) would randomly assign roles to volunteer participants. Then we'd have a night phase, where the thread is locked, and all of the chosen mafias may converse with one another through PMs. They then send a message to the game master with who they want to kill that night, and the day phase begins, and the town may talk among themselves. The day phase lasts until everyone has voted on who to lynch that day, or if they want to kill nobody at all. Optionally, the game may start with a day phase.
A couple problems I can see with this is that one of the dead may talk during the game and disrupt discussion (or just anyone that isn't actually in the game), that and anyone can PM each other at any time, but that's basically just the whisper mechanic. A dead still won't know anyone's roles, however, so this isn't much of a danger unless a handicapped maf outs themselves to a dead person.