The "Day of the Barney Trilogy" is a very notable Hate Fic of Barney & Friends that has Barney commit Corruption of a Minor on a large scale, personally maim and kill people, rape teenage girls after taking them under his wing as his Special Friends and impregnating them with mutant offspring that they die giving birth to, cause every catastrophe in world history, and it's still darkly humorous.
The Team Fortress 2 fanfic "Surrogate" contains a scene which, whether or not you can bring yourself to laugh, is clearly structured like a comedy. There's a literal dead baby involved, and Medic thinks he wants to know where it's gotten to. Heavy doesn't want him to know, but, unfortunately for them both, is a Bad Liar.
Banette: All I remember was everything being white for as far as I could see. I don't know if I imagined it all, if it was a dream, or if I really died. What really surprised me was that there weren't any flames.
Banette: Oh come on, you didn't honestly think I was gonna end up anywhere else if I died, did you?
The Harry Potter fanfic "A Black Comedy" is full of examples, but one that stands out is this exchange that seems to intentionally run down the checklist.
Harry: (My mother) died when I was one.
Harry: (Trying to salvage the awkwardness) My dad too.
The "Long live the king" line spoken during Mufasa's death has become an Internet meme. Just search through Google Images or any image site and you'll find at least a dozen photos (usually of cats) with this line tacked onto them.
Hobbes: Just a weird guy telling chicken jokes and road jokes. They were about as exciting as a chicken crossing the road.
Calvin: Unless the chicken got hit by an oncoming car.
Hobbes: That would be sick.
Used, appropriately enough, by Sirius Black in Another Perspective. After being found innocent of the crimes he was imprisoned for, Sirius runs into Crouch (who threw him into prison without a trial) at the Quidditch World Cup.
Crouch: You may have convinced the Boy-Who-Lived you're innocent but you'll break the law again and be back in Azkaban in a heartbeat.
Sirius: Could you put me in my old cell? It has a wonderful view of your son's burial place.
In the rewrite of Episode 73, Tails refuses to hand Cosmo over to Tsali. Tsali responds by throwing Tails to the floor, opening his ribcage, and ripping his heart and lungs from his chest with his bare hands. Complete with a Bond One-Liner;
The CATverse is described as a black comedy - while the antics of the Scarecrow's three henchgirls are generally Played for Laughs and the series as a whole leans on the comedic side, they still work for a supervillain who routinely tortures innocent people with fear toxin, and innocents are victimized throughout the stories. On the other hand, heavy subjects like bullying and child abuse are treated very seriously in the narrative when they come up, and occasionally the Scarecrow's dog-kicking tendencies are not played for laughs.
In Mabel In Butterhurst, Sebastian cracks up while telling the story of his birth in chapter 2, which involves his father committing suicide right in front of him. The girls don't find it amusing.
There's some pretty dark humor in The Story To End All Stories, which is evident right from the opening scene in which Barney the Dinosaur is unceremoniously killed off.
Ultra Fast Pony frequently cracks jokes about racism and off-screen character deaths. Probably the blackest moment comes in "Pinkie's Day In", where Pinkie Pie accidentally kills two babies through incompetent parenting. And it gets lampshaded:
Mrs. Cake: Well, this series took quite a dark turn. Pinkie: Yeah, even I feel kinda bad making jokes about dead babies.
Purple Days sets King Joffrey (of GOT/ASOIAF infamy) through a time-loop. At first mostly for the comedy of his dying over and over and over again, sometimes in really over-the-top ways, because of his cruelty and stupidity. Eventually he gets a clue and starts the long road towards real character growth.
The Melinda Chronicles: It's made clear pretty early on Melinda can have a pretty dark sense of humor and she later justifies as a coping mechanism to deal with some of the horrors of immortal life. Comes to a head in Getting Back to Normal when she attends her own fake funeral and gives her own eulogy complete with intentionally over-acted breakdown after peeking in the empty casket. She also once describes her immortality and Healing Factor as making her "this close to a cartoon character".
Christian Potter Chandler uses copious amounts of this and blue humor. One example is Barb giving Chris a nutshot so Bob buys her stuff.
One of the one-shots in A Lot of Pokeballs has Ash' older Pokemon warn the Alolan newbies about the insanity they'll get into by staying around Ash... And then it quickly devolves in the veterans discussing which of Ash and theirs' deaths and near-deaths count.
Rowlet: "Hey, since I become a ghost-type when I evolve doesn't that mean I die?"
The omake series has the Gold Saints dealing with the False Rape Accusation, to hilarious and rather dark effects. It starts with Aries Mu stealing all Legendary Weapons and teleporting himself home, leaving Melromarc exposed to the Waves of Destruction and the wrath of their neighbours, and ends with Aphrodite proving once again that the only reason Deathmask appears to be crueler is that he's more blatant.
In Juxtapose, the author takes the opportunity to fill his comments section with hand puns after someone gets their hands cut off.
"Speaking of themes, how do you like the handsy theme? Am I being too heavy-handed with these puns? You have to hand it to me, I'm pretty good at dropping them! Not that it's an effort, I actually have my hands full handling all these hand puns! Somebody give me a hand in carrying them! Oh, Shiggy, you want to give me a hand? Sure, I hope you don't get your hands bloody in doing so. Blood is a pain to clean out of the floor, and not all of us have Minor Banishment like Izuku. Wait, you didn't know that Izuku has Minor Banishment? Oops, now you do, but things have gone out of hand!"