We have Arya unknowingly play who is heavily implied to be Sansa or Shae in a Bravossian play based on the start of the War of the Five Kings and the part Tyrion played... albeit demonizing him as a Richard III type cackling villain.
Alayne's new friend Myranda Royce is the main source of CMOF in the chapter:
Myranda: The first Lady Waynwood must have been a mare, I think. How else to explain why all the Waynwood men are horse-faced? If I were ever to wed a Waynwood, he would have to swear a vow to don his helm whenever he wished to fuck me, and keep the visor closed.
Also when discussing about the Open Secret of Lyn Corbray's need of money and ambiguous sexuality:
Myranda: Do you think if I asked nicely Ser Lyn would kill my suitors for me?
Alayne: He might, for a plump bag of gold.
Myranda: Alas, all I have is a plump pair of tits. Though with Ser Lyn, a plump sausage under my skirts would serve me better.
Again in Alayne's chapter, Alayne asks about Lyn Corbray's brother, whose young new wife is pregnant.
Lyn Corbray: He remains at Hearts Home with his peddlers daughter, watching her belly swell as if he were the first man who ever got a wench pregnant.
In Arianne's second chapter, she is exasperated by her little fourteen-years-old cousin Elia Sand, who her father sent to her as a lady-in-waiting, but the girl just keeps getting in trouble in a very Arya-like fashion. Given Arianne's past exploits, her complain is Hypocritical Humor:
Arianne to Daemon Sand: Why would my father inflict her on me?
Dowager Lady Mertyns: The same way our smallfolk were persuaded to give you all their crops. Melons or maidenheads, its all the same to your sort. If you want it, you take it. If you should see this Lord Connington, you tell him that I knew his mother, and she would be ashamed.
Princess Rhaenyra: My half brothers would be more to his taste.
When Unwin Peake, Hand of the King, wants to betroth his daughter Myrielle to his king, Aegon III, the boy asks what will happen if he doesn't like her. Unwin says that Aegon only has to wed her, bed her, and make a son with her, and then says, "Your Grace does not like turnips, but when your cooks prepare them, you eat them, do you not?" Soon, everyone in the Seven Kingdoms starts calling poor Myrielle "Lady Turnips". Gyldayn quips that she never became Queen Turnips.
Tyrion Lannister is practically a walking, drinking, wenching Crowning Moment of Funny.
"Tyrion found it disheartening to realize so many strangers were eager to kill him. Perhaps this had not been such a clever plan after all."
"Tyrion was about to tell his father how he proposed to reduce the Vale of Arryn to a smoking wasteland, but he never got the chance."
Barbarian: How would you like to die, Tyrion son of Tywin?
Tyrion: In my own bed, with a belly full of wine and a maiden's mouth around my cock, at the age of eighty.
At the Lannister camp, Tywin is listing their multiple enemies on various fronts: the Starks, Lord Beric, Stannis, Renly, etc.
Tyrion: Take heart, Father. At least Rhaegar Targaryen is still dead.
From one of Tyrion's ADWD chapters: "The ship groaned and growled beneath him like a constipated fat man straining to shit." Write What You Know, eh Georgie?
When Tyrion is on the auction block... "and one!"
Tyrion bidding on himself when he is being auctioned off, as a slave:
"Five thousand is an insult!" Tyrion called out. "I joust. I sing. I say amusing things. I'll fuck your wife and make her scream. Or your enemy's wife if you prefer, what better way to shame him? I'm murder with a crossbow, and men three times my size quail and tremble when we meet across a cyvasse table. I have been known to cook from time to time. I bid ten thousand silvers for myself! I'm good for it, I am, I am. My father told me I must always pay my debts."
Tyrion has something of a habit of chiming in during discussions that other people are trying to have about him as if he's not there.
While it's used as a horrible means of humiliation for Tyrion, the dwarf joust show is pretty funny. It involves two dwarves riding a pig and a dog, exchanging colorful insults and getting confused about which mount belongs to which. In A Dance With Dragons, Tyrion meets Penny, one of the dwarf jousters, whose brother was killed because he resembled Tyrion. Penny complains that she had nowhere to go, she only knows how to mount comic joust shows and that needs two dwarves... Tyrion sees right through her intentions and refuses blatantly to participate. The next chapter starts with Tyrion riding the pig.
A few examples from the Night Watch:
The Night Watch sets up straw dummies as bait for wildling arrows, and name them after different members. Pyp explains to Dolorous Edd that the straw man named for him had been leading the count until the last sortie, whereupon another "man" got three arrows to take the lead.
He continues by complaining that the man the winner was named for was lucky because he completely missed the rocks when he fell off the bridge with an axe in his head.
Edd: I never win anything, the gods always smiled on Watt, though. When the wildlings knocked him off the Bridge of Skulls, somehow he landed in a nice deep pool of water. How lucky was that, missing all those rocks?
Grenn: Was it a long fall? Did landing in the pool of water save his life?
Edd: No. He was dead already, from that axe in his head. Still, it was pretty lucky, missing the rocks.
Dolorous Edd's dialogue, every word of it, can be considered a Funny Moment personified.
When complaning about the cold and thinking of jumping into a pot of boiling water:
Edd: Though I would sooner it were wine than water. There are worse ways to die than warm and drunk. I knew a brother drowned himself in wine once. It was a poor vintage, though, and his corpse did not improve it.
Jon: You drank the wine?
Edd: It's an awful thing to find a brother dead. You'd have need of a drink as well, Lord Snow.
Pyp mocking Melisandre at dinner, thereby making the men of the Night's Watch chortle.
Pyp: The night is dark and full of turnips. Let us pray for venison, my children, with some onions and a bit of tasty gravy.
Hodor often livens up Bran chapters, aided by Martin's narration. Standouts include the line "'Hodor', Hodor said doubtfully" and when Bran tells him to stop hodoring.
There's also this gem in a conversation about Coldhands:
His elk? said Bran, wonderstruck.
His elk? said Meera, startled.
His ravens? said Jojen.
Hodor? said Hodor.
It's not really funny that he gets beaten up badly for it, but after Theon takes Winterfell, he makes a speech to everyone there and basically asks if anyone has objections to his being in charge now. Hodor angrily shouts out "Hodorhodorhodor!"
While Theon's chapters in A Dance With Dragons aren't exactly a laugh riot, there's a funny line in the middle of one of the chapters, where he's thinking about camp followerseuphemistically called "washerwomen". "... Some of them even did some washing."
[Hot Pie]: "Pia says she saw something in the buttery."
The whole concept of Skagos is kind of funny. Unicorns are typically associated with the most idealistic of fantasy, which makes it amusing (and typical of the series) that the location where unicorns are found is a Place Worse Than Death the thought of which scares even jaded Westerosi. Also, the few details about unicorns shown so far, suggest they aren't the friendliest of creatures.
Stannis' put down to Jon in A Dance With Dragons- You haggle like a crone with a codfish, Lord Snow. Did Ned Stark father you on some fishwife?
Every time Stannis makes something that could be interpreted as an attempt at humor. His "jokes" are so absolutely unfunny they instantly become classic.
Stannis does have a few instances of humor, if unintended. His tearing down of Janos Slynt, for instance.
Bowen Marsh: Who better to command the black cloaks than a man who once commanded the gold, sire?
Stannis: Any of you, I would think. Even the cook.
"Laws should be made of iron. Not pudding."
In fact despite his reputation for having no sense of humor Stannis delivers some really cutting put downs:
Renly: A year ago I was scheming to make the girl Robert's queen, but what does it matter? The boar got Robert and I got Margaery. You'll be pleased to know she came to me a maid.
Stannis: In your bed she's like to die that way.
"Her own father got this child on her? We are well rid of her, then. I will not suffer such abominations here. This is not King's Landing."
"I can only hope to win the north by battle. That requires stealing a leaf from my brother's book. Not that Robert ever read one."
Stannis' dry, sarcastic and relatively modern (for the reader) humor is almost inconceivable in a world like Westeros. It's made even clearer when Stannis is one of the few characters that simply doesn't think that fools are funny, but others think they're hilarious.
"Every once in a very long while, Lord Tywin Lannister would actually threaten to smile; he never did, but the threat alone was terrible to behold."
This makes for a nice bit of black comedy in AFFC, when Tywin's corpse is slowly drying out, causing the muscles of his mouth to shrink and tighten. Thus, for the entirety of his vigil and funeral (which is open-casket, by the way), his mouth is pulled back into a wide rictus grin, much to Cersei's continued annoyance and Jaime's mild amusement:
Jaime:"He seems to enjoy being dead."
One very early in the first book: before he leaves for the Wall, Jon gets Arya a sword as a present. Regarding learning to use it, he helpfully says: "First lesson: stick them with the pointy end."
In-universe, Ned laughed when he asked Arya what she knew of sword fighting and she told him that, but agreed with the logic of it.
Becomes a Tear Jerker later on, when Arya is running for her life, and confronted with someone who's going to take her back to her enemies. In a panic, all of the sword fighting lessons that she's had go right out of her head, "and the only lesson that she could remember was the very first lesson, the one that Jon had given her." It turns out to be enough.
In a bit of black comedy/mood whiplash, Jon thinks of the line when he is (possibly fatally) stabbed in A Dance With Dragons.
During a conversation with Tyrion, Tywin refers to Varys as "That cockless wonder."
Alliser Thorne at one point tries to use eunuch to put down Varys in A Clash of Kings, to which Littlefinger chimes in with "To his face, we call him Lord Eunuch."
Something between this and a Heartwarming Moment and a Crowning Moment of Making You Say "Awww!": the list of kings, houses and such in the appendix contains, as of Dance, such charming entries as "Lady This, died screaming in the black cells", or "Ser That, died of the bloody flux", or, "her enemies, false friends and uncertain allies", or "Vera, his axe" (all names anonymized to prevent spoilage)... but also, with Tommen: "his kittens, Ser Pounce, Lady Whiskers, Boots".
And "Lysa Arryn, slain with a shove" on the House Stark page in A Feast for Crows kinda takes the dismissive-black-humor cake.
Sharna's husband is simply referred to as Husband on the Brotherhood page in Storm of Swords because none of the POV characters who have met him knows his name.
Half the things that come out of Tormund Giantsbane's mouth are hilarious. Mostly dick jokes, but they still raise a smile. Har!
An example would be "If a man does not use his member it becomes smaller and smaller until one day he wants to piss and can't find it".
And Tormund ranting at Jon Snow for being a turncloak, including throwing his mug at him, but not before draining it first as he's not someone to waste good mead.
Then after hours of swearing, threatening, and insulting Jon, he immediately starts acting like Jon is a drinking buddy.
Both times Mance sends Tormund out so he can't talk to Jon alone.
Mance: Come inside. The rest of you, wait here.
Tormund: What, even me?
Mance: Particularly you. Always.
Patchface's ramblings about life underwater suddenly become much funnier when you remember a famous song...
Maester Yandel, author of The World of Ice & Fire, mentions having been found abandoned as a child and taken in by an archmaester who claims he might prove of use. Setup for some great destiny? Actually the archmaester was writing a paper on swaddling infants and needed a guinea pig.
It seems Mr Martin had a bit of fun with the Family Theme Naming of some of the historical members of House Tully. There's Lord Grover, Ser Elmo, Ser Kermit and Ser Oscar. They're all Muppets!