Peter,
How about "THE ASH GROVE" (which comes to mind because I posted a variant version to the Guy's Song Circle yesterday)? "BELIEVE ME, IF ALL THOSE ENDEARING YOUNG CHARMS" certainly fits the bill. In a darker mood, what about "CARRICKFERGUS" and its sisters and its cousins and its aunts, like the many variants of "The Water Is Wide"?
This isn't a folk song, but what about Chevalier's "I REMEMBER IT WELL" from Gigi? Or, from Carousel, "When The Children Are Asleep" -- ( "We'll think what fun that we had, / And be glad that it all came true; / You'll still hear me say that / The best dream I know is you!")
I'll be 62 in a month, so I can tell you one thing for sure about getting older: it beats ALL HECK out of the alternative! I'll keep thinking about this one, and get back to you. There may be a lot more out there than immediately springs to mind. By the way, do you know why it takes us "alter kochers" so much longer to retrieve things from memory? (Nod to Dick.) Because of the size of the database.
L'Chaim