I saw an intersting idea on an archery forum, it's a school project (I would have loved to have such a teacher !).
They tried (and manage) to make whistling arrows... and I think their idea is adaptable to sling projectiles.
Here is what they've done. It take a small container made of hard plastic, and we can use a fishing lead instead of the arrow's shaft, maybe nailed on to keep it from moving too much.
For the US inhabitants, the little plastic thing they used is something you can't import
It's from an egg of milk and white chocolate with a little gift/toy inside the plastic egg. Great fun, blame the FDA
Everyone else may have recognised "
Kinder surprise" eggs...
I can't try it (can't find the right leads...), somebody is willing ?