The irony of the time of the murder is that it takes place during the carnival season. This carnival could be, though the story doesn't specify, the Mardi Gras, the day before Lent that often is celebrated with a big party before the period of penance that precedes Easter.

In any case, we learn that a big celebration is going on. Montresor's servants have gone off to attend it, despite being told not to, and Fortunato is dressed in a festive costume that consists of a "tight-fitting parti-striped dress" and a cone-shaped hat decorated with bells. In other words, he is dressed up in a jester's or fool's costume and ready to have a good time. He doesn't expect, on such a joyful night, to be walled up to die in a dark catacomb. Montresor, however, is counting on Fortunato's guard being down precisely because of the drinking and spirit of fun at the carnival.

In the last lines of his story, Montresor tells his audience that for "half of a century no mortal has disturbed" Fortunato's bones behind the brick wall at the back of the burial vaults belonging to his family.  Thus, we learn that it has been about fifty years since Montresor committed the murder. 

Irony is created when there is a discrepancy between expectations and reality.  There is dramatic irony when the audience knows more than the character; verbal irony is when someone's meaning is the opposite of what they say (verbal irony often employs sarcasm); situational irony is when the irony is derived from unexpected events (for example, when the firehouse burns down or the police officer gets mugged). 

The chief irony surrounding Fortunato's death is that he was murdered in the midst of "carnival season." Carnivals, broadly speaking, are celebrations of life. Typically, during carnivals, people gather to party and enjoy themselves. The fact that Fortunato was murdered during the carnival season, then, subverts the very meaning of holding a carnival.