When Does "A League of Their Own" (1992) Take Place?
"A League of Their Own" is a historical fiction comedy film written by Lowell Ganz with Babaloo Mandel, Kelly Candaele, and Kim Wilson that released July 1st, 1992. So when is "A League of Their Own" set?
It takes place in the year:
We know this because it tells the story of various characters who join the real-life All-American Girls Softball League (the name of which was almost immediately changed to the All-American Girls Baseball League), which only existed from 1943 AD to September 5th, 1954 AD. So it must be during or after 1943 AD and before September of 1954 AD.

1943 AD
We know this because it tells the story of various characters who join the real-life All-American Girls Softball League (the name of which was almost immediately changed to the All-American Girls Baseball League), which only existed from 1943 AD to September 5th, 1954 AD. So it must be during or after 1943 AD and before September of 1954 AD.
Furthermore, there's a time and place setting title card superimposed over the footage just after the "WILLAMETTE, OREGON 1943".
More specifically, the "LIFE" magazine cover shown on screen with a photo of Dorothy "Dottie" Hinson (loosely inspired by Dorothy "Dottie" "Kammie" Kamenshek [1925-2010] and Helen "Cally" Callaghan [1923-1992]) taken in a scene just previous is dated for "June 28, 1943". In the real world the league's first try-outs happened on May 17th, 1943 AD. So the story's main action begins in May of 1943 AD.
Near the end of the narrative someone loudly announces, "First game of the first ever women's baseball World Series! This is history in the making, folks! History in the making!" Strictly speaking, the AAGBL did not have a "World Series" but there was a final series of five playoff games in the 1943 AD season (and the real-life winners match what audiences see later in the movie). This happened in the real world in autumn of 1943 AD. After the game is over, a sign outside the park can be seen that clearly says, "SEVENTH GAME SEPT. 26th 1943". So it is certainly September of 1943 AD.
Additionally, there is a frame narrative including opening scenes depicting Dottie heading to the ceremony at the opening of an exhibit devoted to women in baseball at the Baseball Hall of Fame. The ceremony itself is then seen in the closing scenes. This occurred in the real world on November 5th, 1988 AD. So the prologue and epilogue both certainly take place in November of 1988 AD.
This episode of the History in Film podcast examines its exact setting.
It was adapted to TV in 2022.

