First up is Douglas Dumbrille, who played Governor William Claiborne in a 1951 production of the 'Hallmark Hall Of Fame' - "The Pirate And The Lawyer". It's a role he also played in the movie universe back in 1938 in the original version of "The Buccaneer".
Claiborne was the territorial governor of Louisiana who had dealings with privateer Jean LaFitte.
Milton Frome played the Kansas governor (but left unnamed) in "The Pied Piper Of Dodge City", an episode of 'Bat Masterson'. That episode definitely takes place in June of 1883, as it was about the famous Peace Commission photograph of Masterson, Wyatt Earp, Luke Short and other peace-keepers.
It would be nice to know the lady wears an honest crown."
Frome also played Governor DeWitt in "That Taylor Affair", an episode of 'Riverboat'. But they can't be the same man since 'Riverboat' took place on the Ohio, Mississippi, and Missouri Rivers during the 1840s. Forty years earlier and too far away, but I suppose an argument could be made that they might be related... at least in Toobworld.
(The plot of that episode sounds like a doozy - Holden Grey, captain of the Enterprise, got the "bright" idea to boost fame for the riverboat by kidnapping President Zachary Taylor.)
J. EDWARD McKINLEY
This would be a "Born To Rerun" case with the governors played by J. Edward McKinley. Of the two he played in Televsion, his portrayal of Governor George C. Handley is perhaps better known. That's mostly due to the fervent following for 'The Andy Griffith Show' in which Governor Handley was seen in the episode "The Cannon".
Almost 100 years earlier in the Toobworld timeline, he played the governor in "The Immovable Object", an episode of 'Bronco'. It's a convention in TV for actors to play similar roles in the past and the future. Sure, usually it happens in the same TV series, but Toobworld absorbs them all into one universe.
McKinley also played an Old West governor in the movie "There Was A Crooked Man", but that's a different universe of course.