"The Break"
"The Break" the thirty seventh episode of the second season, was broadcast on 19 May 1958.
In "The Break", Jesse James has just been killed by Bob Ford, and most people in the region haven't heard the news yet.
Jesse James was shot April 3, 1882, so "The Break" would have to happen in April 1882 - if it happened in real life and not the wild west of imagination.