I don't think the Middle East has any organized tournament on any sport that I know of. A tournament that could include countries like Syria, Jordan, Saudi Arabia, Lebanon, Iraq, Iran, Israel, Egypt, Cyprus,Turkey, and the Palestine Authority. The game would of course be soccer because a lot of these countries are actually good in it and their fans are passionate about the game. The sporting forums like the Olympics and the World Cup are too far and too few in between for these countries to come in regular contact with each other and usually these matches are so hyped up because of that one chance meeting. And yes, I have faith that Palestine will finally be a country, with contiguous borders and not a swath of bantustans.
We could have other countries join the Middle East soccer tourney, like the USA, England, France, Russia, and Australia which have large numbers of citizens of the Jewish diaspora and Middle Eastern descent. This will also give us the alternative of having a venue outside of the Middle East, which might be needed for security reasons and to build trust initially. The Middle East tourney could be held every two years, like the Africa Cup of Nations.
I know that a number of skeptics will look at the list of countries and roll up their eyes and say a mere soccer tournament will not bring all these countries together. In the Middle East it is most practical to have limited goals. Participation is voluntary. If Iran and Israel do not want to participate, that is alright, but they have been invited, and there is more a chance of their soccer teams meeting on the field then there is a chance in a million of Mahmoud Ahmedinejad and Ehud Olmert meeting up at this point. Iran did meet the Great Satan in the World Cup, in 1998, and it was considered a success in terms of soccer diplomacy as the players came out to play and not engage in fisticuffs.
Michael Ledeen, William Kristol, anyone of those "lets bomb Tehran" warhawks out there to give credence to this proposal? No. I thought not. It is just a mushy lefty pipedream.