The exact time frame is not known because Saki is not specific in this tale. But it seems to be in the early 20th century, due to the country home setting, which many Edwardian families of the upper level owned.
No specific dates are mentioned, but it's been assumed that it takes place in the early twentieth century, most likely during the reign of King Edward VII. The where part of the setting is much easier since it's entirely set in one room of an English country home that belongs to Mr. and Mrs. Sappleton.
It is in the early 1900s, you can find this in the interactive reader plus book. All you need to do is to seek the preview of the story which will be found just before the begining of the story.