Faulkner gives his reader only one exact date in "A Rose for Emily." At the beginning of the story, he writes that Miss Emily's taxes were "remitted" in 1894. At this point, Miss Emily's father would not have been dead for long, and the mayor most likely told Miss Emily that she did not have to pay taxes because of her isolation as a single woman and because she represented the "aristocracy" of the town.
Based on that year, Miss Emily meets Homer Barron several years after that--near the turn of the century (1800 to 1900), and has a brief relationship with him before he disappears. At the story's end, as the curious townspeople enter the deceased Miss Emily's room, the narrator states:
"Already we knew that there was one room in that region above stairs which no one had seen in forty years."
The closing off of the room and Emily's house from the town occurred after Homer's disappearance, so you could argue that with adding on the forty years to 1900 (give or take a couple of years) that Miss Emily died somewhere around the late 1930s or early 1940s.
In regards to the last post, just because a work is published during a certain decade, it does not dictate that events in that work cannot take place in the future. Authors often include events that are outside of the publication time of their works (whether those events be centuries early or decades later).