I don't know if they fit your definition of singer-songwriter, but both Eric Clapton and Mark Knopfler play nylon string guitars on occasion. EC most famously on some of his Unplugged session tracks.
Woody Guthrie isn't with us anymore, but there are one or two photos of him holding a nylon string guitar. He was of course the paragon of folk singer-songwriters, especially among the folk revivalists of the 50s and 60s.
Well, not that many people are old enough to remember American "guitar culture" much before 1950, though it goes back to the conquistadors and colonists. There's a book called "The Guitar: An American Life" by Tom Brookes--as much homage as history.
Sales of most things in America boomed in the 20 years after world war two--nylon string guitars would have been no exception. They didn't actually exist until after WWII anyway, come to think of it. I'm sure many were bought, for many reasons. Television, beatniks, Segovia and colleagues, flamenco, all probably contributed to its popularity, among other things, along with the folk revival.