Here's my Pony Iraq plan, as seen through the eyes of Gene Roddenberry and his Star Trek TOS writers:
We have Captain Kirk order Scotty to beam all the warring leaders into Muqtada al Sadr's office, and then demand they all work together or the "Federation Coalition" will fit them all with "concrete galoshes."
Then, if they doubt our sincerity and power, order Scotty to set the Enterprise's phasers to stun, and blast Baghdad with them, thus knocking unconscious all of the various militia memebrs in combat situ.
The reaction to this show of force by Bela Oxmyx and Jojo Krako...er....I mean...Muqtada al Sadr and Jalal Talibani, etc. will allow Kirk to appoint al Sadr the "boss" of Iraq, with perhaps Maliki as his lietnenant.
Then Kirk must demand a "piece of the action," with our "cut" amounting to 25% of the oil revenues generated. We would then set aside that money in a special UN trust fund for Iraq in order to "guide [them] toward a more ethical system."
Now, just make sure that Dr. McCoy doesn't leave sample of weaponized smallpox in al Sadr's office, or in a few years the Iraqis [a "highly imitative people"] may be demanding a piece of OUR action.
Problem solved. No muss no fuss.
ADDENDUM: Or, we could bluff the warring factions into believing that we built up the Green Zone with a highly volatile element called Corbomite, and....