Ciel taking in Snake, despite lying to him that he was looking for his friends when said friends had attempted to ambush Ciel's mansion and were killed by Ciel's staff. However in later chapters, it's shown that Ciel does geniunely care for Snake, such as the brief encouragement he gives to Snake when other people were mocking his appearance. Also, he told Snake to get on the rescue boats in his place.
Season 2 Episode 11: Alois (in Ciel's Body) asking Hannah to tell him that she loves him and give him a hug. Which he's always needed. She does both, which prompts him to cry tears of joy and say "Love is...warm, isn't it?"
In episode 1 of season 2, Alois begs Claude not to leave him alone, and Claude holds Alois's face in his hands and declares he'll never leave him alone.
Alois's final wish results in Ciel's immortality. Aww!
Sebastian's and Ciel's exchange at the end of chapter 65 of the manga. This is the first time we have seen Ciel being genuinely concerned about Sebastian and treating him with kindness. True, Sebastian is a demon, but the little scene at the end is very sweet nevertheless.
In chapter 66, Ciel cheats during the egg hunt by pretending to have an asthma attack in order to distract Soma and Agni. Their reaction after losing because of his ploy? They are happy Ciel is well.
In chapter 70 MacMillan going into Ciel's bed to be next to him while they have their talk.
After learning that Ciel has been aiming for the batter's face in Cricket the crowd starts booing about blue house's poor sportmanship. How does the P4 of the oppossing team, the power based green house, respond? Greenhill gives the crowd a reason you suck speechdefending Ciel's actions on the basis that aiming for someone's face requires a lot of practice and the use such underhanded tactics is just proof that blue house really is serious about the tournament winning this year.
Agni's backstory. The son of a corrupt brahmin, he spent his life indulging himself and casually breaking the law until it came down on him. As they prepared to hang him, Soma - for no reason other than his own whim - jumped onto the gallows platform and saved his life. Agni's Undying Loyalty suddenly makes a lot of sense.
"And at that moment, God appeared."
Chapter 91, Finny's flashback and speech to Ciel.
The story about when Ciel gave Finny his name is really touching. Especially since having a name means so much to Finny: his name has given him a whole new identity and allowed him to become something more then a disposable test subject. "You taught me how to grow," indeed.
There's one chapter where the Phantomhive three are talking about how far they've come, and how much they owe Ciel and Sebastian. Doubles as a tearjerker, because none of them have any idea that Sebastian's a demon and they're just being manipulated, but it's still touching to see how they feel.
In episode 3 of the Book of Circus, one of the Scottland Yard officers buys a bundle of flowers from a little girl because she reminds him of his daughter, Emily. Too bad the girl gets abducted by the Noah circus troupe minutes later and the policeman (and all his colleagues) get brutally murdered for trying to save the girl.
The very ending of Kuroshitsuji III: The spirits of Joker, Peter, Wendy, Jumbo, Dagger, Beast, and Doll entering what is presumably Heaven. Nuff' said.
Chapter 96.5 (That Butler, Friendly) is probably the most heart-warming thing in the manga. We get to see a little bit of the Circus members' history together when Freckles loses a tooth and, rather than letting Peter tell her that the tooth fairy isn't real, Joker and co. go out and earn a coin to give to Freckles when she wakes up. It gets even more heartwarming when Freckles uses that money to buy them all bread. They recount this story over dinner with Sebastian and Ciel on the two's first night at the circus, and it genuinely seems like the circus members have bonded with them. Becomes sad when you realize that all of these characters die brutally for a cause that was worthless in the end.
In chapter 99, Sieglinde has become a Broken Bird after finding out the horrible truth and accepts Ciel's offer to kill her. However, Ciel never intended to kill her and instead convinces Sieglinde to live and use her gift to create "magical medicine" while escaping the forest with him.
Though, it should be noted that Queen Victoria did give Ciel a request to bring Sieglinde to her, so YMMV on whether Ciel was genuinely inspiring Sieglinde or really playing mind games with her.
Only if the live-action movie is considered canon, but at least there is a chance that Ciel will grow up and have a family with Elizabeth before having his soul eaten. To bad that it doesn't just end with Ciel, though.
In the live-action movie, Sebastian feeding Shiori the antidote before she dies was almost this, until he goes on to say he only revived her because her soul wasn't dark enough and that eating it at that time would be boring/unsatisfying.
Though, knowing that despite everything, Shiori is not that far gone yet could count as heartwarming itself.