The structure of "A Rose for Emily" is a bit different from most stories in that, in typical Faulkner fashion, the story just ENDS with a shocking discovery that has been foreshadowed from the start.
The rising action is the set-up to the story. We are given all pof the background about Miss Emily, we are given the stories about her and her father, about Homer Baron, about the rat poison and the smell that came from her place.
The climax is when they find the hair on her pillow. Everything in this story leads up to this moment.
The falling action is unstated, really, as this is told in a flashback format. You could almost look at it as occurring only in the reader's reflections on what has occurred.