==== Spoilers from The Christmas Pig ====
As it happened with the Harry Potter books, J.K. Rowling does not give an exact timeframe for The Christmas Pig. But there may be a way to try to, at least, set time boundaries for this story. It is in Chapter 46 (“Power’s Plan”) when we have a clue. It is there when Memory says:
“Sixty-nine years ago, […] my mistress and her sister, Amelia Lousie, went to see a movie called The Fugitive”.
The Fugitive is a 1993 film, starring Harrison Ford and Tommy Lee Jones. The first thought is to think the book is happening 69 years after the release of the film, in 2062, but that would be wrong. As the Christmas Pig explains in Chapter 20, “Time’s different in the Land of the Lost. They say an hour in the Land of the Living is a whole day in the Last of the Lost.”
There are two options from here. Thinking that Memory was lost right after her mistress watched the movie (which seems to be the most possible scenario), or was lost recently (which wouldn’t make sense since she seems to have been in the Palace for a long time now). If Memory was lost right after her mistress watched the movie, it means that 69 years have passed in the Last of the Lost. Sixty nine years are 25.201 days, so that means 25.201 hours in the Land of the Living.
So, 25.201 hours is roughly 1050 days. The Fugitive was in cinemas during August 1993: 1050 days later would be July 1996, which is not possible since this is happening on Christmas Eve. But of course, Memory could have been lost in December of 1993, and that would work.
With only these facts it seems impossible to know when The Christmas Pig is set. At least we know that the story is taking place between 1996 and… 2062.