I’m in my late thirties and it was still in common use in India, and perhaps specifically among Anglo Indians? But it meant more like “no chance”.

“Can I go out to the movies with my friends?”

“Nothing doing! You have an exam tomorrow”

Or failure to do something.

“I tried to fix it myself but nothing doing”.

Looney Toons / Merry Melodies also bear out this connotation quite well