The willow and poplar trees will work for your essay.  The most significant tree in the novel is the pomegranate tree. Amir first mentions it in Chapter 4 and narrates that he and Hassan carved "Amir and Hassan, the sultans of Kabul" (Hosseini 27) into the tree'strunk.  The tree is the scene of most of Amir's reading to Hassanand serves as the location for Amir's seeking Hassan's revenge after he betrays him in Chapter 7.  Amir feels so awful after he allows Assef to rape Hassan that he wants Hassan to respond in anger to him or to show some emotion.  Thus, when Amir and Hassan go to the tree after Chapter 7's event, Amir pelts Hassan with pomegranates hoping that he will respond with the same violence, but once again Hassansimply takes Amir's hostility and anger.

At the end of the novel, when Amir first returns to Kabul, he insists on revisiting the tree.  It still stands, but is now barren (like the country of Afghanistan, like Soraya'swomb, and--at this point in the novel--like Amir's soul).  Amir notices that the tree still bears the carving of his and Hassan's names.

When discussing the pomegranate tree (or the other trees) focus on not only the events that occur near the trees but also on the trees' appearance, their specific literary symbolism in other works, their color's significance, and themes that are normally associated with trees or plants in general.  Good luck!