If if the Jewish leaders would have done it themselves (a point of contention as to whether or not they had the authority to do so under Roman rule) they would have stoned him. But they *wanted* this particular kind of death...because of the Jewish custom that every man who was hung up on a tree was cursed. (Deut 21:23) They wanted him to be a cursed man...they figured that no Jew would *ever* accept a man who had hung on a tree as their Messiah. They didn't realize that this also played into fulfillment of prophecy.
That is a fundamental misreading of the text from Deuteronomy. Here is the entire passage: "21:22 If a person commits a sin punishable by death and is executed, and you hang the corpse on a tree, 21:23 his body must not remain all night on the tree; instead you must make certain you bury him that same day, for the one who is left exposed on a tree is cursed by God. You must not defile your land which the Lord your God is giving you as an inheritance."
He wouldn't have been cursed by the hanging itself; the curse would have been as a result of not being buried the same day. And the point against this was that the land not be defiled by burying something that was cursed. But according to the Gospels, Jesus was buried the same day so this is irrelevant. Doubly irrelevant, since the passage from Deuteronomy has nothing to do with crucifixion, which is death by hanging on a cross, but with hanging up the body of someone who is already dead. Furthermore, there is no evidence from the Gospels that such a thing was even thought of by the Jews, so this whole proposition is strange at best.
I honestly believe that Pilate tried to free Jesus because he thought the idea of executing this man for nothing was nothing short of ludicrous. When he realized this was essentially an internal dispute that boiled down to nothing more than jealousy...he washed his hands of the whole thing. He was the only Roman of importance that ever had anything to do with it...and he didn't want to have anything to do with it.
This assumes that the Gospel accounts of Jesus's trial are accurate. Which I seriously doubt.
Pilate is known to history as a horribly cruel and unjust man. The portrayal of him in the Gospels is as a wishy-washy person who was afraid. I can't speculate as to what really happened, but I know that all of the Gospels mentioned that all of Jesus's followers had deserted him, so none of them witnessed any such trial (as if they could have if they had wanted to).
The Gospels portray "the Jews" as feeling that Jesus committed blasphemy. If this was true, they would have been well within their rights to execute him by stoning, and Pilate wouldn't have cared. But that isn't what happened. He was crucified, which was a Roman punishment for all kinds of things. The most likely thing is that he was crucified because he was a public nuisance, including the "scourging of the Temple", during Passover Week. That would have been reason enough, there is no reason for a Sanhedrin conspiracy.