Phillip is courageous in The Cay by Theodore Taylor several times. First of all, he showed courage when the ship he and his mother were on was torpedoed. It took a lot of courage for a boy to do what he had to do at that moment. Many children would panic under the same circumstances. Many adults would too.
Once he and Timothy reached their cay, at first Phillip acted like a spoiled brat and used his new blindness as an excuse, but when he realized Timothy was trying to teach him how to survive, he changed. Phillip had been afraid to climb a tree to get coconuts, but one day he decided that he was going to do it. It definitely took courage for him to climb without the benefit of sight!
Phillip showed the most courage after Timothy died, and he was left alone. He had to do everything for himself. Timothy had warned him about the danger of the pond where he could find langosta (small lobster), and Phillip had not tried to catch any before Timothy's death, but when he no longer had Timothy there to do it for him, Phillip was able to catch them himself. He survived all alone until he was finally rescued, and that takes a lot of courage!