Why eliminate the .22 Short?
Because the original challenge was "name one POPULAR..."
The .22 Short hasn't been popular since the Coolidge administration. Or earlier.
Anymore, .22 Short is available largely only through speciality stores or online.
I've not seen .22 Short in a gunshop in over 20 years; I've not seen .22 Short in a store other than a gunshop (local hardware store used to sell ammo when I was a kid) since I was a kid.
"WIthout looking them up, there were a couple of rimfire cartridges that are approaching that 150 year mark, though I suspect it has been a long time since they were commercially available. There was at least .44 Henry. Anyone want to name another ('cause I can't think of one)."
Yes, there are any number of .25., .30, .32, .38, .41, .44, .46, .50, and .56 caliber rimfires that are, or are very close to, 150 years old.
And, other than one of the .32s (.32 Long Rimfire, I think), none have been in production since before World War II, and many dropped out of production before World War I.