Chaplin was more visual comedy, what we might call “slapstick” now. For written comedy you can consider Mark Twain.
Be mindful that 100 years is just a short time ago. That was the heyday of Dorothy Parker’s acerbic wit and the Algonquin Round Table.
Eddie Cantor was huge star in the 1920s. The following link is a 1923 “talkie” of his “song and dance” routine: A Few Moments With Eddie Cantor. 1923 Fun Film - YouTube
That’s right.
It even works in (some) other languages, with a little adaptation.
A few weeks after showing her the sketch for the first time, my older daughter asked me about the possibility of translating the sketch into German to share with her classmates (most of her classes are taught in that language). A quick google and I found these two guys from several years ago who did a (partial) translation as their own school assignment.
YouTube link hidden behind text because of error about embedding media
Listening to it, my daughter (who is much more fluent in German than I am) observed that the grammatical trick behind the sketch is largely interchangeable in this language. She noted a couple of places where an English-specific pun had to be dropped or modified, but she was impressed at how well it adapted (and we then discussed how a surprising amount of English has its feet on German ground).
Then she ran off to her room to see if she could make it work in French. 
For starters, when the dog’s tail is poking out a hole in the seat of his pants.
I think the brilliant parts are still brilliant. One problem may be that other parts of his films haven’t aged well and/or weren’t very good to start with. They seem too simple or obvious and end up dampening the mirth generated up to that point.
Another problem is that many people can’t relate to things that are too old for their tastes. Some of the best music of all time can be found on old recordings, but some people only hear scratchy, low-fi noise.
For me and I think most people, appreciation of art involves an initial stage of skepticism, as if someone were knocking on your door and you decide to have a look and maybe let them in.
The main difference is now things are funny until someone gets hurt. Back then things were funny because someone got hurt.
There’s a joke that I first read in the humor pages of Playboy that I later read in the 14th-century book The Decameron (the one that involves the husband climbing a tree).
Another Decameron comic sex-themed story (about a barrel) previously appeared in 2nd-century Roman novel The Golden Ass (or The Metamorphoses) by Apuleius.
Some jokes never die; they just slowly change with the times. Especially the smutty ones, because people by and large don’t change with the times.
Aren’t all of the stories in the Decameron sex-themed?
Most of them, but not all of them are comic. Some are also about drinking/gluttony instead.
Did she have to try translating it from baseball into some other context?
It seems to me that it should translate fairly easily into any language and any context. Baseball in the original just provides a set of roles, but any other set of roles could work just as well: “Who’s the center, What’s the name of the goalie, I don’t know the coach”, or “Who’s the CEO, What’s the name of the chief engineer, I don’t know the receptionist”. And since half of each pun is a proper name, and the names are rather implausible anyway, you can just take whatever words your language uses for “who”, “what”, and the like, and declare those to be (implausible) proper names (at worst, if you’re in a culture with a short, rigidly-proscribed list of acceptable names, then you set the joke Over There, in foreign parts where they do things differently).
I’ve seen a version of “Who’s on First?” about computers, which uses names of computer software instead of the who/what/I don’t know terms.
I’ve seen several bits that were either variations on, or inspired by, Abbott & Costello’s “Who’s On First” (including one involving the band The Who). But IMHO there’s a limit on how much you can change and still consider it a translation of the famous routine, as opposed to a different routine inspired by it or along the same lines as it.
The rock band version is pretty funny, IMO. https://www.youtube.com/watch?v=Mdqv5xIsFLM
An earlier rock version, with three bands instead of two: https://www.youtube.com/watch?v=ludCVowT-DE
Vin Scully was delighted when Chin-Ling Hu made it to the big leagues with the Dodgers in 2007, especially after he hit his first single.
I cringe to link to Quora for obvious reasons, but it seems like a non-terrible answer—
I believe it translates to “Wenn ist das Nunstück git und Slotermeyer? Ja! Beiherhund das Oder die Flipperwaldt gersput!”
I’m surprised by people not laughing at Chaplin. I have myself laughed out loud at many of his slapstick routines from his old silent films. Maybe you just don’t care for Chaplin.
Buster Keaton’s The General was mentioned upthread. I highly recommend it – we showed it to our daughter when she was little, and she loved it (despite being silent. And black and white). But that;s just one example. Keaton in general (and Harold Lloyd) were great silent comedians, and I find them very funny.
As for earlier humor, I agree about Twain. (That’s not his only piece about Cooper, BTW. There’s also this –http://strangebeautiful.com/other-texts/twain-coopers-prose-style.pdf ) A lot of Twain’s stuff is still funny. Heck, the man was known as a humorist. Try A Connecticut Yankee in King Arthur’s Court Read the original. This book hasn’t been appropriately adapted yet on TV or the movies.
I will agree that humor and styles change, and that something that was rip-roaringly funny to one generation might leave another unmoved. But I was delighted to find that one of my grade school teacher’s assertion that ancient comedic material wasn’t really “funny” ("it just means it has a happy ending, she explained) wasn’t at all true. As the jokes cited above show, some things stay funny for a long time.
Read the epigrams of Martial sometime. First century CE