The title "A Rose for Emily" which is connotative of love, romantic passion, and beauty contrasts with the gothic elements of obsessive possession, irrationality, and death in Faulkner's story. This, then, is the irony.
First of all, Emily's concept of love is perverted by the domination of her father whose Old South patriarchy does not allow Emily to find a husband worthy of her. Repressed by her patriarch, Emily loses her sense of self and womanly passion. After her father dies, she greets the aldermen who "rose [the only mention of this word] when she entered" with a "cold, dry" voice indicative of someone who is herself dying. Subjugated so long to this patriarch, Emily, dressed in black and looking like a "bloated" corpse, wears her father's watch--lost in his time--standing before his portrait as she rebuffs these men who have called on her.
Later, when she remerges into society, she is seen with a man from the North, who likes to be around the young men of the town. This appearance causes the townspeople much consternation as they recognize that Emily's companion is incongruous to her station in the town; as they comment, she has forgotten noblesse oblige. When Homer Barron (ironic last name) leaves town and then returns as though resurrected after "three days," Emily, in her tragic irrationality, purchases arsenic to ensure that he will never leave again.
The horrific ending underscores the irony of the lovely title. Rather than a beautiful rose, symbolic of love, romantic passion and sensitivity, there lies a skelton of Homer with a single, dead grey hair--not a rose--upon the bed in the dusty room.