The setting of "A Very Old Man with Enormous Wings" is an incredibly vague setting. There are specifics about the setting that we can talk about; however, Márquez does not give a specific, geographical location for the story's events, nor does he provide readers with a date or date range.

This works to the overall advantage of the story, because the story's genre is magical realism. It weaves believability with fantasy elements. Readers are given a realistic seaside town, but it is filled with magical elements, like a man with wings. Having a less specific setting aids with selling the magical parts of the story.

If you need a very specific, concrete setting, then the entire story is set in Pelayo's courtyard. Despite that very limited setting location, readers can gather some additional information about the town itself. Based on the story's opening sentence, the town itself is near the seaside. We are told that Pelayo is throwing crabs back into the sea. The names of the characters are Spanish-sounding names, and Márquez is a Columbian author, so it does make sense to assume that the story is placed in a town on the Columbian coast.

As for the time period, readers aren't given enough details about technology to place it within a specific decade. The carnival's appearance doesn't help either, since that kind of thing has been popular and going on for hundreds of years. If I had to guess, I believe that the story is placed in the 1920s, and this guess is based on the information about Elisenda's shoe purchase:

Elisenda bought some satin pumps with high heels and many dresses of iridescent silk, the kind worn on Sunday by the most desirable women in those times.

That style of shoe was popular in the 1920s.