There are many examples of verbal irony in "The Cask of Amontillado." One of my favorites comes as Montressor lures Fortunato deeper into the catacombs and pretends to talk his guest into withdrawing. Fortunato will have none of it.
“Enough,” he said; “the cough's a mere nothing; it will not kill me. I shall not die of a cough.”
“True—true,” I replied...“
The irony is that Montressor knows exactly how Fortunato will die, and as Fortunato jokingly remarks, it will not be from a cough.
My other favorite example comes when Fortunato asks Montressor if he, too, is a member of the secretive order of Free-Masons.
He laughed and threw the bottle upwards with a gesticulation I did not understand.
I looked at him in surprise. He repeated the movement—a grotesque one.
“You do not comprehend?” he said.
“Not I,” I replied.
“Then you are not of the brotherhood.”
“You are not of the masons.”
“Yes, yes,” I said; “yes, yes.”
“You? Impossible! A mason?”
“A mason,” I replied.
“A sign,” he said, “a sign.”
“It is this,” I answered, producing from beneath the folds of my roquelaire a trowel.
“You jest,” he exclaimed, recoiling a few paces. “But let us proceed."
Poe has fun with the double-meaning of the word "mason," allowing Montressor to produce a trowel (a brick mason's tool for which he has later plans) to serve as an ironic twist for use as a secret sign for members of the brotherhood.
There are three types of verbal irony: sarcasm, overstatement, and understatement.
Sarcasm is saying the direct opposite of what you mean for humorous effect.
Overstatement (also known as hyperbole) is exaggerating what you mean for humorous effect.
Understatement (also called a litote) is minimizing the importance of what you are saying for humorous effect.
First of all, any use of "amontillado" is a kind of overstatement. It does not exist, so any mention of it is an exaggeration, a lure, and a ploy.
Here are some other examples from the story "The Cask of Amontillado":
"I have my doubts," I replied; "and I was silly enough to pay the full Amontillado price without consulting you in the matter. You were not to be found, and I was fearful of losing a bargain."
The speaker, Montressor, says that he has "his doubts" about finding Amontillado. This is obviously a lie, but it is also verbal irony. Specifically, it is understatement: he is pretending not to know if he has the real wine so as to lure Fortunato into his trap, a kind of verbal baiting.
"Come," I said, with decision, we will go back; your health is precious. You are rich, respected, admired, beloved; you are happy as once I was. You are a man to be missed. For me it is no matter. We will go back; you will be ill and I cannot be responsible. Besides, there is Luchesi" --
The narrator pretends to care about Fortunato's health. This is sarcasm: he wants to kill him. Just as there is no wine, there is real possibility of going to Luchesi. Monstressor is only pretending to care about his victim of revenge as a misdirection ploy so as not to alert him to his true feelings and plans.