In writing a letter of this sort, we will want to first decide what exactly Carlson and Curley might want to change about themselves.
Carlson is the character who kills Candy's dog. Though he says that killing the dog is in everyone's best interest, including Candy and including the dog, he may be viewed as acting selfishly. He may also be seen as cruel. These are traits that he may want to change. He may even want to apologize for shooting Candy's dog (though he did get permission from Candy).
Curley is more thoroughly negative than Carson. Curley starts fights, treats the men on the ranch poorly, and treats his wife poorly too. He is a petty tyrant who abuses the power of his position and seems to act out of a sense of insecurity. He is also vengeful. These are all traits that Curley might repent of in a letter about how he would change his ways.