One of the claims that Dr. King makes in "Letter from a Birmingham Jail" is that it is time to take action against the oppression of African American people and that his nonviolent methods of protest are justified. He states, "We have waited for more than 340 years for our constitutional and God given rights" (you can cite pages from your text using MLA format).
The appeal that he uses to make this claim is mainly pathos, or an appeal to the reader's emotions. For example, he writes that African Americans can't wait to mount their protests because "you have seen vicious mobs lynch your mothers and fathers at will and drown your sisters and brothers at whim." He makes this appeal more immediate and directed towards his audience by addressing them as "you," and this appeal would likely have provoked the pity of his audience. He also includes the following appeal:
When you suddenly find your tongue twisted and your speech stammering as you seek to explain to your six year old daughter why she can't go to the public amusement park that has just been advertised on television, and see tears welling up in her eyes when she is told that Funtown is closed to colored children, and see ominous clouds of inferiority beginning to form in her little mental sky, and see her beginning to distort her personality by developing an unconscious bitterness toward white people.
This example, also an appeal to pathos, or emotion, is particularly wrenching, as it involves the disappointment of an innocent child who can not go to an amusement park because of the color of her skin. He places the reader in the position of being the parent of a child who is denied having fun because of her skin color. Perhaps you can find other appeals simiilar to the above in his letter.