The novel is based in part of Ray Bradbury's memories of his own childhood. Since it was published in 1962, when Bradbury was about 42 years old, the time period is likely between 1930-40, when Bradbury would have been between 10 and 20 years old.
In the book, the ages of the two protagonists is given:
At that time, James Nightshade was thirteen years [old]... William Halloway was thirteen years [old]... Both touched toward fourteen; it almost trembled in their hands.
(Bradbuy, Something Wicked This Way Comes, Google Books)
This would place the date, assuming that Bradbury is the inspiration for one or both of the boys, in October of 1913. Bradbury's child characters are old enough to understand that evil can exist, but still too young to fully comprehend it. They can be afraid, but do not understand the meaning of their fear or how it can affect them in real ways. At that age, the typical human psyche has suffered very few traumas, and is relatively yielding and easily healed. The events of the story are described several times as causing the boys to "age overnight," which refers to the shock on their minds, not their bodies. In any event, the range of 1910-1930, and 1913-14 in particular, would seem to be the most accurate fit.