The White Knight chapter in 'Through The Looking Glass.' The White Knight is considered to be an expy of Charles Dodgson, and he is the only character who is genuinely kind and helpful to Alice, and seems to be fond of her. He also seems to be a bit saner, but that's not saying much. His chapter also has a bit of a more melancholy tone to it than the rest of the books, and at the end of the chapter, Alice is 'sorry to see him go.'
The fact that somebody else finds this scene heartwarming.
The Cheshire Cat, contrary to what most people believe, is also one of the few characters who is genuinely kind to Alice. He even gives her advice on how to survive Wonderland!
When Alice starts to cry over her loneliness, the White Queen comforts her by telling her to consider other things.
"The Wasp in a Wig", a deleted chapter, which survived and can be found in Martin Gardner's annotated edition. It slots in just after the White Knight chapter — Alice, about to cross the last brook and be promoted to a queen, hears a deep sigh, and stops to talk to and comfort the Wasp. Even though his attitude is not encouraging, she thinks to herself, "Perhaps it's only pain that makes him so cross" and persists in making him more comfortable.
The poems found at the start and end of each book. Though they also contain a slight bit of tearjerker, especially the ones that frame Through the Looking-Glass.