On a personal note, I find the verbal irony throughout the story humorous in an almost uncomfortable way. When Fortunato tells Montresor not to worry about his health, for he "shall not die of a cough," Montresor replies "True, true." Of course, we know that Montresor is leading him to his death, but the fact that he is essentially hinting at his plan lends a very dark humor to the scene. Similarly, each time he warns Fortunato to watch his step, and delights in showing him the mold growing on the walls, it offers a gallows humor rarely matched. Also, as Fortunato's drunkenness increases, his gestures and quips become more and more comical.
One last note about humor in the story (an anecdote, if you'll indulge me): When I was in college at UCLA, I worked in the theatre. Every Halloween, a tribute to Edgar Allan Poe would be produced. Celebrities and musicians would read stories and poems, and one year Will Ferrell read "The Cask of Amontillado." He performed so well, and at the point where Fortunato coughs repeatedly, Ferrell drew the cough out to a full minute's time. He would cough a bit, seem to be about to move on, and then continue coughing. It truly added humor to the story, breaking up the suspense of the narrative and providing comic relief. I've read the story like that a few times to my students, and I'm certainly no Will Ferrell, but I've found that it lends itself as a natural catalyst for laughter.
Although a very disturbing tale of revenge gone too far, there are elements of humor to "The Cask of Amontillado." First of all, Poe puts the bumbling Fortunado in a jester's outfit. Court jesters were paid comedians to entertain kings at at all times; typically, they dressed in very bright, absurd outfits in order to be amusing and entertaining. And, they wore hats that had little jingling bells all over them--so, they jingled as they walked about. Fortunado's particular hat was "conical," so, shaped like a big cone on his head--very comical. It is hard not to be amused, in a sad sort of way, picturing Fortunado in this absurd outfit, jingling around in the catacombs. Poe writes,
"The gait of [Fortunado] was unsteady, and the bells upon his cap jingled as he strode."
So, there is Fortunado's outfit that is a bit funny. Also, Montresor, though not trying to be, is a bit funny at times. He leads Fortunado through the house, which is empty. Normally, the house would have been full of servants, and hence witnesses to the fact that he was leading Fortunado down to the catacombs. How did he get them to leave? He knew their natures well. He states,
"I had told them that I should not return until the morning, and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned."
This is a rather amusing commentary on the situation at hand. Tell the servants they'd better not leave, which ensured their departure. In addition to little quips like this, Montresor's very intensity is a bit funny, also in a sad satirical sort of way. He can't have revenge, he must "punish with impunity." And, how DARE Fortunado "insult" him!! The audacity! Of course the ONLY conclusion to draw is that Fortunado must die a slow, painful, terrifying death. Yes, that's what a sane human being would conclude....Montresor is so extreme in his hatred and avowal of revenge that it is almost ridiculous.
Those are just a few moments of potential humor in the tale; I am sure that there are many more, but that should get you started. Good luck!
Like egraham, I, too, enjoyed the verbal irony. For example, when Montesor encounters Fortunato by design, he exclaims,
My dear Fortuntao, you are luckily met. How remarkably well you are looking today!
Another example of humor in "The Cask of Amontillado" by Edgar Allan Poe" occurs with Montesor's parodying of a mason and his pun upon the word both in a grotesque manner, but at the same time so ridiculous as to be funny--the black humor to which an allusion has been made. And, it is humorous that Fortunato says to Montesor, "You jest," since he understands that Montesor parodies the Masons, but he does not comprehend the significance of this parody.
Added to these references to humor, there is a grotesque parody of lovemaking as the narrator first mentions that he and Fortunato have arrived at the "most remote end" of the crypt where "bones had been thrown down and lay promiscuously..." Fortunato vainly lifts his "torch, endeavoring to pry into the depth of the recess." But, he cannot see, and Montesor throws the chain around his waist, capturing his victim:
'Pass you hand,' I said,'over the wall; you cannot help feeling the niter. Indeed it is very damp. Once more let me implore you to return...
'The Amontillado!' ejaculated my friend, not yet recovered from his astonishment.
Later, Montesor "unsheathes" his rapier and the screams "erected the hairs upon [his] head" as the sad voice of Fortunato cries, "For the love of God, Montesor."
Clearly, in addition to the other instances of dark humor and parody, at the end of the story, Poe parodies in yet another grotesque manner the seductions that must have been going on during the carnival in other dark, clandestine places.
A very good example of humor can be found at the very beginning of the story itself: Montresor had "vowed revenge" against Fortunato. But he decided to mask his real feelings by outwardly appearing friendly towards him - "I continued as was my wont, to smile in his face." This grim irony of situation results in harsh 'black humor' with Montresor remarking sarcastically,
"It was about dusk, one evening during the supreme madness of the carnival season, that I encountered my friend. He accosted me with excessive warmth, for he had been drinking much. The man wore motley. He had on a tight-fitting parti-striped dress and his head was surmounted by the conical cap and bells. I was so pleased to see him, that I thought I should never have done wringing his hand."
The Cask of Amontillado is quite a dark story that revolves around a man who gets revenge in the worst way possible: murder. It is difficult to find a part in the story that is humorous, light-hearted or otherwise. The biggest "humor" part I can think of is Fortunato as a character, with his "funny" sayings and his personality in general.