nitpick:
The Untuchables (TV series) took place in the 30’s. Remember Elliot Ness was fighting Frank Nitti? Capone had been convicted in 1931.
I doubt shows about the period 1890-1940 would do much better. To most of us, that’s right in our national cultural blindspot: not far back enough to be capital-H History, but too long ago to relate to as real life.
Well, there was The Waltons…
That wasn’t so much about the 30s, or even the depression, as about being poor but honest mountain folks. They were meant as stand-ins for an aging generation to look back on and feel good about.
Good point. When I think of that period, all I can come up with is:
League of Nations
Prohibition
Immigration surge
World War I
Stock market crash, Depression, Dust Bowl
Switch from agrarian to industrial economy, rural to urban population centers
Automobiles for everyone
I’ve read some good books (fiction and non-fiction) dealing with some of this stuff, but it’d be hard to make it dramatic (or funny) enough for TV.
The Young riders seemed to be fairly accurate insofar as the props. They did use cap-and-ball Colts and Remingtons, and Plains rifles. I’m not aware of any female Pony Express riders, but ‘Lou(ise) McCloud’ did disguise herself as a boy in the show. ‘Wild Bill’ Hickock was, IIRC a bullwhacker for the Pony Express and not a rider, but (again, IIRC) he either worked with or got a job for ‘Buffalo’ Bill Cody.
Baa Baa Black Sheep deserves a mention…
Um, I uh, meant by being… first, yeah, that’s it, first.
whew.
Then there was the made-for-cable Bordertown, which was better than Dr. Quinn about minimizing modern characterizations. Far from perfect, but less annoying, I’d found.
There’s also Tales from Avonlea.
And a personal favorite, the current series from the BBC: Life on Mars, which is mostly set in 1973. Maybe.
I forgot about The Lost World and Swiss Family Robinson.
The OP pointed out that historical settings are quite common in theatrical films. I think this brings up a major difference between films and television shows. People go to the movies to escape. They want to sit in the dark and be transported to a bigger, brighter world, so they’re willing to be taken someplace exotic, like a foreign country or an unfamiliar time period. In contrast, people watch T.V. for comfort. They are bringing a story into their homes, so they want it to be something familiar that fits in with their lives, and someplace that they can continue to revisit week after week. Miniseries are in between these two poles, so there’s room for a miniseries that takes you someplace unfamiliar, because you’re only expected to be there for a short time.
Of course these are all generalisations, and there are numerous exceptions, but the majority of American television viewers are still looking for shows that are comfortable and relatable, which means set in America either in the present day or in a period that feels genuinely American.
There was “Hawkeye” which was set in colonial America, I’m guessing around the time of the French/Indian War (7 Years Wars to you foreign types) and guest starred Lynda Carter in one episode. Hot hot hot.
There’s “Jack of All Trades” starring Bruce Campbell as an American secret agent teamed up with an English agent to stop the evil forces of Napoleon. Early 19th century.
Marc
That show should make anyone who’s taken a high school social studies class cringe!
Someone may have mentioned it, but I didn’t see it, so I’ll put forward Robin Hood
Also while it only lasted one season, there was the television version of Paper Moon.
Three more came to mind. The Adventures of Dick Turpin definitely comes to mind.
Also Jim Bowie and Riverboat both qualify and are not exactly “Westerns” in the purest sense.
How about Ellery Queen?
Death Valley Days was not a normal Western either.
Well, I don’t think accuracy was a requirement of the OP. 
Marc