Would the Biblical allusions in "Ransom of Red Chief" be ironic or just further describe the ironic situation that a child is terrorizing his kidnappers?

The biblical allusions that O. Henry employs in "The Ransom of Red Chief" do reinforce the overall irony of the story's plot—a child getting the better of his kidnappers—but also feature delightful irony in their own right.
Comparing Red Chief's flinging the stone at Bill to the story of David and Goliath is ironic because by this time in the story, readers likely already feel sorry for Bill and dislike Red Chief. It's the most natural thing in the world for people to take the side of the underdog (the David against the Goliath), yet readers know Red Chief is no hero. He has already pitched rocks at a kitten, after all. As a result, we're tempted to take Goliath's side.
When Bill asks Sam if he knows who his favorite Bible character is, it's ironic on a couple of levels. First, we don't expect an outlaw to have a favorite Bible character. Even Sam thinks the question is a result of Bill's being temporarily knocked senseless. Second, though, Bill's choice of a favorite is one of the worst villains in the Bible—King Herod. Herod tried to kill the Christ Child. Once readers get the joke, though, they can understand Bill's choice. If King Herod had been around at the right time in Summit's history, Bill's tormenter would never have been able to launch the rock that could have killed Bill. 
The third allusion isn't strictly biblical, but it is religious. Bill compares himself to "martyrs in old times. . . that suffered death rather than give up the particular graft they enjoyed." This passage is ironic because it presents martyrs as if they were petty criminals, like Bill and Sam. Bill correlates the tortures he has endured at the hands of Red Chief with the persecution stalwarts of the faith endured for their commitment to God. Bill is no saint, but Red Chief does seem to possess "supernatural" ability to wear down his enemy.
The clever, multi-layered irony of the biblical allusions adds to the humor of "The Ransom of Red Chief."