I had completely forgotten - my favorite childhood book 'Coral Island' by RM Ballantyne has a sling in it - 3 blokes stranded on an island - one uses a bow, one a spear and the protagonist uses a sling...

I wish I paid more attention as a kid! I would have been slinging from 9 years old instead of starting in my late 20's/early 30's (cant remember)

"Thierry la fronde" or in English : Thierry the sling. He's a kind of Robin Wood  with a sling.
It's an old (sixties) black and white TV show. No historical accuracy. Watching recently, I noticed a barbed wire fence on the edge of a field. But nice heroes.
Back then, I was a kid and I liked this TV show.

In the video game Far Cry Primal you can use a sling.

There is an older science fiction series, Dumarest of Terra.  The character grows up on Earth in a post-apocalyptic time.  He hunts with a sling while growing up.  He stows away on a spaceship and spends most of his life as a drifter.  But the series is about his efforts to find and return to his home, to earth.    His main weapon is a knife.  But he often talks about using the sling to stay alive and he uses one from time to time as an adult.  Author E.C. Tubb