While fighting with Greg, Rabbit softens immediately once he sees Lily. Twice, actually.
Singing her a lullaby
Calmly but firmly telling her to go inside and not look back, knowing he's about to get beat up by the Free World.
Rabbit's final moment with his mother, as they reach a mutual understanding, is a warm relief after all their angst.
The bouncer giving Rabbit props after his first battle definitely counts. He started the film antagonizing Rabbit for being white but came around to respect him. It's a subtle moment, but powerful.
Similarly, if you look closely, you can see Lil Tic congratulate Rabbit after his battle with Lyckety. Lil Tic was the rapper at the beginning of the movie who made Rabbit choke. Bonus points for Lil Tic being played by Proof, Eminem's real-life childhood friend.