I will focus on Hassan and Amir to provide examples of courage from The Kite Runner. You will notice that early in the book there are examples of Hassan's courage and that it is not until later in the book that we see any examples of Amir's courage.
On pages 41 and 42, Amir and Hassan are faced with Assef, who has brass knuckles, and his friends,all of them bullies and older and larger than Amir and Hassan. Hassan pulls out his slingshot and faces Assef down, saving Amir and himself from a beating, at the least. His courage lies in the fact that he is scared, but still acts. Amir sees Hassan's fear and says, "He was scared plenty" (42).
When Amir manipulates events so that Hassan is accused of stealing, Hassan admits to the deed, even though he knows that he and his father will be made to leave. This was a courageous action, too.
Once Amir returns to Afghanistan, we see more courage on his part. In fact, just returning to Afghanistan is courageous! Two examples of his courageous actions are his taking on Assef, his Nemesis, after all those years, a man who clearly has great power and who nearly kills him and his taking Sohrab home to American with him. The reunion with Assef, who still has his brass knuckles, takes place in Chapter 22, and Amir says he remembers very little of it, but he clearly endured great physical damage. In a lovely piece of symmetry, what saved him was Sohrab, the son of Hassan, who has a slingshot, too, which he uses against Assef.
Why do you suppose Hassan exhibits great courage from the beginning and Amir does not? It takes Amir nearly the entire book to become brave. Surely, it cannot be because they are from different tribes? They both have the same father. What is the difference between them?