"On Melancholy Hill". "'Cause you are my medicine, when you're close to me..." The music video that goes with it is a CMOH in itself: Noodle's under attack by pirates, Murdoc has a Pet the Dog moment and takes 2D and the cyborg to save her, and everyone who collaborated on the album goes with them. Sadly they don't find her, and they fail to save the manatee.
Also, "To Binge." He loves a drug addict...but loves her...just loves her. "But I just have to tell you that I love you so much these days...have to tell you that I love you so much these days, it's true."
Every Planet We Reach is Dead also gives the warm fuzzies...
Some Kind of Nature (It's Lou Reed and he sounds happy!) and Don't Get Lost In Heaven/Demon Days definitely count.
This clip with Murdoc and 2D. For once, they're actually getting along; Murdoc doesn't attack or even insult 2D. He even compliments him, and the two just happily work together on a song. It's a nice change from the usualhell 2D gets in interviews, and pretty heartwarming.
In the story, there's something sweet about how 2D's dad had the family name "Tusspot" legally shortened to "Pot" before 2D's birth so that his son wouldn't go through the same crap that he did because of it.
2D checking up on Noodle in "DoYaThing", especially the little smile they both get.
It should also be noted that ever since the El Manana incident, Noodle's life has been pure hell (figuratively and literally.) After she had escaped from there, she was almost always violent, angry, hurt, or a combination of all three throughout the Plastic Beach saga. Fast forward to 2012, when we see what the Gorillaz are up to in their new (temporary) home. Noodle only appears briefly in "Do Ya Thing," but when we see her, she's taking a long-deserved rest and looks content for the first time in years.
Also, on a related note, the floating island returns.
It's the first time we see 2D smile since Plastic Beach too. Pity Murdoc hits him with a shoe later.