In "Boxing Daria", when Daria and Jane meet in the diner. Actually, most of the end of Boxing Daria.
"It occurs to me that I wasn't the easiest child in the world to raise, and perhaps I'm quite lucky to have you for parents."
"Didn't know if you need this, but just in case ~Quinn." Considering how much Quinn had been complaining about lugging that box around.
Also, Quinn agreeing with Daria and confirming that she was right about their parents fighting all those years ago. The way she sadly admits that their parents really were fighting about Daria is a genuinely touching moment, as is the concerned look Quinn and Jane share after the news takes it toll on Daria.
Given how oblivious Mr. O'Neill is most of the time, he genuinely wanted Daria to give the tours to the freshmen. While Daria assumes it's because she can make the misfits like her feel welcomed, Mr. O'Neil's point is to demonstrate Daria is not as antisocial as she claims to be. For him is a little moment where he shows how much he cares about Daria as a student.
Any moment when Quinn helps Daria, or vice versa.
In "Is It Fall Yet?", Daria managing to help out a troubled child who she identifies with. Aww.
Stacy and Tiffany admitting that of coursetheyknew Daria was Quinn's sister. They just didn't say because they could tell it was what Quinn wanted.
There's also the possibility that when Tiffany said "We were just trying to be polite", she was saying that she and Stacy were being polite to SANDI, being the only one truly unaware of the truth, and not wanting her to feel stupid.
Ms. Barch, the man-hating harpy science teacher, shedding a tear and realizing that Mr. O'Neill is actually sensitive in "The Daria Hunter".
Daria in "Gifted", when she has her conversation with Jodie who confesses her chafing at being "Queen ofthe Negroes" at school and wishing to be more like Daria and her fearless candor. At that, Daria confesses that she occasionally wishes she could be more like Jodie and when Jodie is flattered by that statement, you see Daria respond "I'm not saying all the time", with that small smile that she grants only to the people who deserve it.
In "I Loathe A Parade" Jodie gets fed up with the hypocrisy of her and Mack being elected Homecoming King and Queen every year, as well as how humiliating she finds standing on a float in a poofy dress waving to the crowd. Just as she and Mack decide they're sick of playing along with the charade, she sees a young black girl in the crowd waving and looking at her with shining, hopeful eyes. She smiles and promptly stands up again to keep waving.
Mack: What happened?
Jodie: Oh, what the hell. We may be tokens, but we're damn good looking ones.
"Lucky Strike": When Quinn, in front of the whole class and with not a trace of shame, defends Daria to the other students and admits that they are sisters. Even if everybody already knew it.
When Quinn asks Daria to make the test easy because she doesn't want her friends to hate her, Daria says: "Why should you go out of your way to protect the stupid? You're not one of them".
A very short moment as the episode is ending, in which Jeffy, one of the popular jocks, tells Daria that he thinks she is a good teacher. Daria responds that she thinks some of them aren't half-bad students. While it was clear she was mostly referring to Quinn, the fact that she complimented Jeffy's original argument earlier shows real growth on her part.
In "Write Where It Hurts", Daria is supposed to write a story about people she knows but can't come up with anything good. After an earlier argument, her mother notes that Daria often hides her feelings from everyone and advises her to write a scenario the way she would like it to play out, as opposed to her usual combination of sarcasm and Brutal Honesty. The story is a fluffy little piece about the family, set in the future when everybody is successful, happy and more well-adjusted. And after hearing it, her mother breaks into tears and gives her a hug.
In "Through Lens Darkly", when Daria locks herself in the bathroom stall because she doesn't want to admit to her vanity when she gets contacts, and no one other than Brittany comes in and tells Daria that she's glad that she got contacts. Brittany took it to mean that they weren't so different, because Daria getting contacts meant that even she, a person who prized herself for her intellect rather than her physical appearance (or a "brain" as Brittany put it), cares about her looks. This made Brittany feel less shallow and feel that Daria was a human like everyone else. Her words were convincing enough to make Daria come out of the stall and thank Brittany for them - even if Brittany claimed to have gotten such words of wisdom from wearing a pair of fake glasses.
Mr. O'Neill and Mr. DeMartino sharing a cry at the Liquid Dinner after Mr. O'Neill confesses that he's scared of Ms. Barch roping him into marriage in "Is It College Yet?". It's one of the rare times that Mr. DeMartino shows that he has feelings (besides frustration and rage over his idiot pupils and his miserable life).
In "The Old and the Beautiful", where Daria is put with a deaf person to spite her when she's complained at for reading. When she almost leaves after getting angry upon realising she's deaf, the woman grabs her arm and tells her not to leave. I got the impression that she was put in there and ignored by her family or friends and had nobody visiting her; so she was just glad that somebody was visiting her.
In "Too Cute", Daria tried to tell Quinn that she didn't need plastic surgery and admitted that she looks great.
When Daria comforted Quinn after she got rejected by her tutor, in "Is It Fall Yet?". Made even more heartwarming by the fact that the rejection actually was rather heartbreaking, because at that point (and definitely in this movie), Quinn had already become much more sympathetic.
Daria's graduation speech, where she admits that despite high school sucking, it can be improved with the help of a good friend, a loving family, and lots of pizza.
After having been apart for the whole summer, and fighting for weeks before summer started, seeing Daria and Jane smile and reconcile at the end of "Is It Fall Yet?" definitely brings a smile to your face.
In "Ill", all of Daria's closest classmates (Kevin, Brittany, Mack, Jodie), along with Jane and Quinn, come to visit Daria in the hospital after learning she is sick. Even though Kevin and Brittany thought it was a "brain disease", it was still nice to see them show up for her.
The campers cheering on 'Uncle Anthony' during "Is It Fall Yet?". Because of the connection he makes with the children, he rediscovers that spark that made him want to be a teacher in the first place.
In one episode, the Fashion Club has their caricatures done at a fair, and they threaten to sue the artist for what they claim to be "defamation of character". After failing multiple times to have any sort of legal action brought against the artist, Quinn consents to just burning the picture. But, as it turns out, neither Quinn or Sandi has the drawing. It turns out that Stacy kept it and has it hanging in her closet, because the artist drew her in a positive light compared to the others.
In "Mart of Darkness", Daria and Jane spend all day chasing down a wholesale club employee that turns out to be Andrea, who had been avoiding them due to how they usually act and fearing what they'd do once they found out. Instead, they treat her normally and keep her job a secret. She even smiles for once.
From "Is It Fall Yet?", Quinn answering Mr. DeMartino's question on Manifest Destiny correctly, with her own little Quinn-esque touch to it. DeMartino is genuinely touched that one of his students, Quinn Morgendorffer of all people, actually gave a correct answer, right after he announced that his faith in teaching was reinvigorated. His faith was rewarded and it's one of the few times DeMartino has been legitimately happy without someone suffering.
DeMartino: Ah, Quinn, that's very good! Thank you for making my day rewarding.
In "Monster", Daria and Jane make a movie about Quinn, mocking her shallowness. However, at the end of the episode, Daria edits the movie in order to portray her in a more positive light, after Quinn tells them that she's looking forward to seeing her video, hoping that it doesn't make her look stupid because she knows that acting shallow and being obsessed about fashion and popularity is silly, but it's what she does best.
Daria unbending a little at the end of "Groped By An Angel", by acknowledging that Quinn has a right to her newfound spirituality, even though Daria doesn't believe in it due to lack of proof.
The handful of times where Trent shows just how close he is to his little sister, Jane.
The original focus of the episode "Pierced" was that Trent wanted Daria to help him pick out a birthday present for Jane, and at the end of the episode when his gift turned out to be a song he had written for/about her.
At the end of the episode "Daria!" after Trent sees that Daria and Jane are unharmed, he immediately hugs Jane first.
In the beginning of the episode "Dye! Dye! My Darling" it shows that Jane and Trent are at the zoo together just the two of them and immediately afterward Jane thanks Trent for going along with her. At the end of the episode after Jane and Daria have a falling out, Jane is walking alone when Trent drives up in his car and tells her that they "need to go for more rides" together. After Jane gets in his car Jane confides in Trent about her troubles with Daria and he gives her some legit advice and he even tells a little joke to get her to smile.
Although not exactly 'heartwarming', in the episode "Lane Miserables" Jane doesn't think twice about handing over her toothbrush when Trent asks if he can borrow it.
The mere fact that he always affectionately referred to his younger sister as "Janey".
In "The Misery Chick", Jane has been avoiding Daria in the wake of Tommy Sherman's death, due to her guilt over a joke she made about him dying. She hides out in her room sketching, telling Trent to tell anyone who asks that she's out running. When Daria shows up to try and talk to her, he at first goes through with the lie, but quickly realizes that Jane and Daria need each other right now, subtly guiding Daria upstairs by telling her he might not have heard Jane come home. Daria even realizes what Trent did for their sake. It's a small touch, but a very sweet, brotherly moment for Trent.
In "Aunt Nauseam", Helen and her two sisters have been at each other's throats the whole episode. Daria notices that Quinn has been acting strangely and is trying to spend time with her, complimenting her and asking if she wants to watch Gone with the Wind with her. At first, Daria ignores this, but after Helen, Rita, and Amy make peace, Daria realizes that the reason Quinn has been trying to spend so much time with her is because Quinn - the same Quinn who would tell people Daria was her cousin who lives with her or a weird neighbor girl who hangs out at their house - doesn't want to have a bitter, angry relationship with her sister when they're older. The penultimate scene of the episode is the girls watching the movie together, and promising that they won't turn into their mother and her sisters.
In "It Happened One Nut", Trent realizes that Daria was embarrassed to be working at the peanut stand (and would be humiliated if he, in particular, saw her) and quickly changes his mind about eating there in order to spare her feelings.
Helen and Jake treating Trent as one of their own in "Lane Miserables". It's probably the first time in his whole life he's had parental figures that actually gave a damn and provided him with some guidance in his whole life.
In the musical episode, Helen calls the Lanes to see if Daria and Jane are there, and when she realizes Trent is home alone and has done nothing to prepare for the hurricane, she tells him to come over, because he'll be safer with them. Her immediate concern for him is very sweet.