In an odd way, the exchange between Percy and Brutal after Arlen's execution qualifies. As depressing as it is to spend your life working as an executioner, it's pretty damn heartwarming that Brutal still has enough heart to think of the prisoners under his charge as human beings, and that he actually cares enough about them to speak up when someone takes joy in killing them.
During John's execution Paul is willing to let John go without the hood because John is afraid of the dark.
The cops' friendship with John in general. They take him to see a movie, something he's always wanted to do, the day before his execution. And as John stands before the electric chair feeling the hatred from the parents of the girls he was accused of killing, Dean tells him to focus on how he and the others feel about him.
John getting in on The Mouseville hoax after saving Del's mouse.
John watching the "flicker show", seeing Fred Astaire and Ginger Rogers dancing cheek to cheek in Top Hat; even the nice symbolic touch of the camera slowly tightening on John's face, with the light from the film projector creating the illusion of heavenly rays behind his head.
John: Why, they's angels. Angels, just like up in Heaven.
Even more heartwamring when most of the Mile Guards are sitting with him. If not for the fact that it took place in death row, you'd think the group were just taking their friend to the movies. Made even more touching when Toot, who's mostly sarcastic and joking around during execution rehearsal is working the projector.
When John is in the execution room, he's confronted by the audience. Among them, is the parents of the girls that were murdered. Brutal figures out he's empathically feeling their hate and helps him through it.
John Coffey: There's lotsa people here that hate me, lots. I can feel it. It's like bees stingin' me.
Brutal: Well feel how we feel then. We don't hate you. Can you feel that?
The entire plot to help Melinda Moores. Paul even muses, in the book, about how John Coffey must know that "in the normal course of things, [Hal Moores] would pick up a pen and sign [Coffey's] death warrant." Coffey saves her anyway.
Reverend Schuster, the pastor who comes down to Cold Mountain to pray with and comfort the condemned before they walk, is a Crowning Momentof Heartwarming all by himself.
Paul keeping Mr. Jingles, just like Del wanted him to.