Answer:
it is quite ironic because he did end up dead due to the cough. he claims about how silly it would be to die of a mere cough, yet he dies from it.
edit for correct answer:
it is ironic because in this scene Montresor knows that Fortunato will not die of the cough since he will be the one to kill him. a big part to look more into is the symbolism in the coughing fit. the coughing represents Fortunato's persistence. he is in a damp moldy room with weak lungs but persists through showing his strength.
(aplogies if anything is wrong, i havent read the play/book, i only went over some summaries)