The date of "The Jeweled Gun"
"The Jeweled Gun" was the tenth episode aired, on 24 November 1957, a date which is starting to seem almost as distant - 61 years instead of 81 years - as the episode's fictional date of 1876 was in 1857.
This episode opens with a shot of tombstone giving the dates of Mr. John Harris as 1841-1876, and the narrator says that the grave is empty. Bart's adventure ends up with him impersonating Mr. Harris and getting "killed". There is another shot of the tombstone, and the narrator says the (fake) funeral was on a late Wednesday afternoon in May, 1876.
Any perpetual calendar will show which day of the week was on which dates of the month in 1876.
Sundays in May, 1876 included May 7, 14, 21, and 28.
Mondays in May, 1876 included May 1, 8, 15, 22, & 29.
Tuesdays in May, 1876 included May 2, 9, 16, 23, & 30.
Wednesdays in May, 1876 included May 3, 10, 17, 24, & 31.
Thursdays in May, 1876 included May 4, 11, 18, & 25.
Fridays in May, 1876 included May 5, 12, 19, & 26.
Saturdays in May, 1876 included May 6, 13, 20, & 27.
https://www.timeanddate.com/calendar/?year=1876&country=1
So anyone who watches the episode and notes which day of the week is mentioned for the funeral will have a choice of only 4 or 5 days in the 19th century that the funeral could have been held on.
Going by the ages of James Garner and Jack Kelly in 1957, Bret and Bart would have been born about 1837 and 1836 respectively, though they might have been younger than their actors.