Hagakure's first scene in his social link has this little gem when he attempts to predict Naegi's future:
Hagakure: Your child and my child...will share the same mother!!
Naegi: No! I will never allow it!!
Want to know something funnier? Make the wrong choice and this ends up happening at the end of chapter 5.
In chapter 2, Monokuma attempts to motivate the students to commit murder by threatening to reveal their "darkest secrets" to the entire world unless one of them commits a murder. The funny one is Naegi's, simply because it's such a banal "darkest secret" compared to the eventual culprit and victim's secrets: Naegi used to wet the bed until 5th grade.
Genocider Syo is a goldmine for these; using Makoto as a punching bag during a Relationship Values moment, and describing Togami's underwear with a Godot quote come to mind.
Hagakure's rant about how his fortunetelling has nothing to do with the occult, or cattle mutilation, or alien abducted burgers.
Hagakure: Do you get it now?! That's the true meaning of cattle mutilation!
"Who the hell are you?!" "Ah, I'm the mastermind." "Nice to meet you!" "Nice to meet you too."
Your mileage may vary on how much this example is "funny", but during every one of Monobear's executions, Monobear deliberately inserts a humorous event into it. Chapter by chapter, here they are:
In chapter 1, after Leon Kuwata is executed, we get a montage of everyone having shocked faces at how cruel the execution was, and Monobear's own shocked face appears in the lineup
In chapter 2, Monobear begins Mondo Oogawa's execution with his own copy of Mondo's "corncob pompadour" hairstyle.
In chapter 3, before Celestia Lundenberg can burn to death at the stake, Monobear turns the whole thing into a ridiculous farce by sending a fire truck to put out the fire, complete with big honking sign shouting "Help! Help! Help!" and after the fire truck rams Celes to death, Monobear puts out the one tiny remaining flame with a fire hose.
In chapter 4, as Monobear is using a bulldozer to crush Alter Ego's laptop into a ball, we get some brief shots of Monobear joyfully messing with the controls as though he's playing a videogame.
In chapter 5, the chalkboard professor-Monobear is using to teach the about-to-be-crushed-Kirigiri-or-Naegi a lesson changes midway through. It starts off as a diagram of the crushing machine the conveyor belt is pulling them towards, but midway through the execution video it starts off as a special life and conception lesson.
In chapter 6, usually, before the executions happen, we get an 8-bit "game over" clip of Monobear dragging the culprit away by his/her head to be executed. Before this execution begins, however, we get the same 8-bit "game over" clip, but this time Junko Enoshima voluntarily just stands up and walks away with Monobear. Then, she puts herself through all the previous executions, and humorously lives through all of them. She survives Leon's execution because she doesn't chain herself up and she manages to bat away all the balls at hyper-speed, she survives Mondo's execution because she's stoic while dizzy with her arms crossed and not turned into butter, she survives Celes' execution by meditating like a yoga master in the middle of a friggin' burning stake, she survives Alter Ego's execution by having her pigtails deflect the bulldozer, she survives the space journey because the rocket launches up and down in an instant arc, and...finally, just before the crushing machine finally kills her, she's not pinned to a desk by her hands, she's just hugging Monobear and smiling at the viewer while doing a "V" victory sign.