Definitely a Military Tribunal in Baghdad ... not something in a federal court in NYC.
I would think the firing squad would be on the table also.
The last soldier executed after military trial for desertion was Pvt Slovak during WWII for desertion ... I believe.
Slovik
Since he did not desert, that would not apply, however the last to die was in 1961.
http://en.wikipedia.org/wiki/John_A._Bennett