Examples of Irony:
1. The boy who is considered the weakest at Devon--Leper--is the first to enlist in the war effort. Granted, Leper does not make it very far in the training process, but his initial decision to leave school and enlist surprises everyone.
2. It is also ironic that Finny's second "accident," the fall down the steps, causes him to break the same leg again. This is ironic and symbolic. It's as if Gene injures Finny a second time.
3. At the novel's end, the doctor explains to Gene that Finny died during surgery when marrow--representative of life and living life to the fullest in literature--causes a blood clot of sorts which stops Finny's heart. It's as if Finny is so full of life that it kills him.
I think one good example of irony in the book is the name "Super Suicide Society of the Summer Session." It is an ironic name because because Finny ends up dying as a result of the club's actions. Afterward, Gene feels as if he has died too. The club's name winds up not being such an innocent and harmless name.
A second example of irony within the book is the character of Leper. He is portrayed as a weak character, and he is the character most likely to fight in the war only if drafted; however, Leper becomes the first boy to join the war effort because he volunteers to join.
A third example of irony is that Gene is the person who bounces the branch, which ultimately leads to Finny's death. It's ironic because Gene is supposed to be Finny's best friend. Finny trusts Gene more than any other boy at the school, and it's unexpected to readers that Finny's most best, most trusted friend winds up being the cause of his death.