We know for sure that Robert Louis Stevenson's adventure novel, Treasure Island, took place some time during the 18th century, though the author does not specify an exact date. In his narration, Jim Hawkins writes that it was

... in the year of grace 17--...

The date "1745" is mentioned in the log of Billy Bones, and Stevenson includes the dates 1750 and 1754 on his treasure maps. According to one source, the action of the novel probably takes place between the years 1757 and 1762. There are many other historical allusions which put the date of the story some time in the mid-1700s. 

• Admiral Sir Edward Hawke became a household name in England following his victory at the Battle of Cape Finisterre in 1747.
• There is the suggestion that England is at war with France, which would put the time period somewhere between 1740-1763 (either the War of the Austrian Succession or the Seven Years' War).
• Since the Hispaniola visits a friendly port in Spanish America, England must have been at peace with Spain, who entered the Seven Years' War in 1762.
• Since one of the treasure maps is dated 1754, and Captain Flint supposedly had been dead for about three years, the novel could not have begun before 1757.

What specific year does "Treasure Island" take place?

Nowhere in the novel Treasure Island does Robert Louis Stevenson give us an exact year that this story took place.  We can tell from the very beginning of the story that it is sometime in the 1700’s.  “Dr. Livesey, and the rest of these gentlemen having asked me to write down the whole particulars about Treasure Island, from the beginning to the end, keeping nothing back but the bearings of the island, and that only because there is still treasure not yet lifted, I take up my pen in the year of grace 17__ and go back to the time when my father kept the Admiral Benbow inn and the brown old seaman with the sabre cut first took up his lodging under our roof.”

You can also trace some of the years by the names of other actual people mentioned within the pages of the novel, by cross-referencing the names with dates.