It only takes this long if you don't use a round timer and you don't allow shared victories. Even with new players we usually wrap up the game in 4-5 hours (people will start getting eliminated around hour 2 - so usually we have a "loser room" with other games and stuff to do).
You can also do it online with a turn a day (I ran an office Diplomacy League this way).
It's worth noting that you can play the game completely openly and honestly. We have had complete victories where the winner never once backstabbed anyone (he was just a very shrewd negotiator). It's just pretty rare because the more honest you are all game, the more reward you will get for a well placed backstab.
Usually I set it up like "The pot is $350. The game is over as soon as all remaining players can unanimously agree on how to split it up."
It also adds much more drama to the end game. If you are down to a small couple of territories and basically out of the game, you might still have a lot of power to negotiate your way into the winner's circle.
IMHO, the fun of Diplomacy is sneaking in little side conversations and hiding in a corner to tell a secret. In person, it's very fun. A better approximation online would be to play asynchronously (like a turn a day) via a website.