At the beginning of the movie they talk about summer is almost over. The 2nd day at the store he is by a calendar on the wall that says August. Then when Charley gets home his sons gave him a card for Father's Day and he said, That's right, Sunday is Father's Day. So that means it would be June.
During the chase scene, while Charley is speaking to the angel, the background is showing a modern car in a driveway when the setting is supposed to take place in 1933.