In Wii Party during Globe Trot, near the end, Max completely stops trying to win, just so Peter can win, to the point of outright avoiding one Hot Spot that would've won him the game so that Peter could have a chance of getting it. Unfortunately, it didn't work, since one of the computers got the final Hot Spot first.
Also in Wii Party, Peter and Max get 100% in Friend Connection, which they claim to have wanted to get for a long time.
A small example in Welcome to Ponyville; when Max goes to see Trixie's show, he says that he really wants to chew Trixie out. However, when the opportunity presents itself, he hesitates, suddenly not so sure he wants to yell at her. He ends up doing it anyway, though.
The Secret Santa in Hearth's Warming Minecraft, where the guys get each other gifts; Peter and Zero are Trolls, with Peter getting Max a wool dildo and killing him with lava and Zero just blows up a nuke for Peter, but Max gets Fury a golden sword of justice and Fury not only sings Zero a song, but also gets him a musket with ammo. Then, at the end, the guys take a picture (screenshot) of them in front of a tree they planted in the crater made by Zero's nuke present for Peter.
In a Tumblr post, Max decides to give an explanation for his suddenstupidity in Tekkit. During his explanation, he says that he considers Peter to be a Tekkit genius.
In Skyward Sword and Super Vexation Saga, Peter goes on about the Creeper plushie Max got him for Christmas and constantly thanks him for it.
Surgeon Simulator 2013: "I am recording this on Valentine's Day; the heart is all that matters!" Even though this was meant to be a pun, it's still a small example.
His third "What the Hell?" Moment for Left 4 Dead 2 actually has a moment of heartwarming. For pretty much the entire video, both Zero and Alec are making fun of Max or getting annoyed by him. However, at about the 3:10 mark, Alec gets knocked down by a Tank and groans about how he needs to get a medpack as Zero revives him. Max, meanwhile, walks over and takes the medpack Alec said he needed, using the excuse that he (Max) had already died once and needed it more. Not even twenty seconds later, Alec gets caught by a Smoker. Max quickly runs up, shoots the Smoker, and uses the very medpack he just took to heal Alec.
The Snowdrop shrine in New Letropolis, and the scene that reveals it. Max goes down a hidden ladder into a large temple-like area, places a rose in a chest, then goes down a secret path back to his house, all while a heartwarming and awesome song plays.
It's a small moment, but in episode 12 of The Drawing Board, Max and Chaz start discussing what members of the mane six they're most like. Max starts to say he's a lot like Fluttershy, only to come to the realization that he lately hasn't been like Fluttershy at all. Real LifeCharacter Development, anyone?
In Max's vlog of CANterlot Con 2013, he finds a rare figurine he wants to buy, but doesn't have the required money on him and is afraid that if he leaves to get more, someone else will buy it. At first, the vendor is willing to hold onto the figurine for him for a bit, but then that turns out to not be necessary; someone nearby buys the figurine for Max and waits for him to get the money to pay him back, so he doesn't have to worry about someone else snatching it up.
In one of Max's Tumblr posts, he goes into further detail about the con, mentioning other moments such as a vendor lowering the price of one of his shirts just for Max because he was a few dollars short. Max concludes that the "theme" of the convention was generosity.
Sonic Spinball of the Super Vexation Saga reveals that Peter got Max a t-shirt with Max's ponysona on it. Max wears it proudly throughout the episode.
Peter being willing to let Max's first try at the game be a practice round, since he hadn't played the game ever before, while Peter is an expert. While some would say this is more "fair" than "heartwarming", none of the games before this had any sort of practice, and Max is usually able to adapt to unfamiliar games rather quickly. So this wasn't so much Peter being fair as it was Peter bending the rules to give Max more of a chance. In the end, though, it didn't help Max win.
In a blog post on FIMFiction, Max reveals why he's been inactive on the site lately. Read for yourself.