I really like the idea of learning slinging by using tennis balls. There are however a few impracticalities with that approach, as pertains to my own situation, so I am considering starting with ping-pong balls. the reason for that, is that I should be able to practice indoors, while I wait for my offspring to finish training.

What I don't know, is if ping-pong balls are too light to use. Has anyone tried slinging ping-pong balls?

Welcome, PingHansen.  I have tried, and yes, they are way to light even for inndoor slinging.  Well, you can do it but you will not be happy.  I would prefer an rolled up sock held together with tape as inndoor ammo.  
These doesn`t bounce around in the room (and under heavy furniture) that bad either
timann

I think the sock is a great idea, and I will surely try using just that - whenever I get my first sling finished 

Using the wrapped paper, I think I'd have to be very careful, as that wouldn't be too far from slinging a wooden block, and not exactly balsa wood either 

Thanks for the suggestions.

Ping.

I may have had sling ping pong ball fights with my friend. 

It actually works surprisingly well with a 25in sling and a fast greek overhand up to around 10 yards (we were slinging indoors, room clearing/tactical slinging). With styles like sidearm the ball is just too light and just falls out. Though if you are just starting out I would go with somthing heavier and more consistent. I have also had sling duels with the wad of paper and tape. And it did hurt (I gave my friend a welt early in my slinging career  ) but you couldn't break a window or anything like that and as long as you have a good backstop you won't have any problems.

Slinging does take a different level of patience than most have so stick with it!

I've slung velcro dotted pino pong type balls at a target in my workshop with a 100% ducttape sling.
Works over about 6 feet - but you lose the balls very quickly

For the first few months I was into slinging I used nothing but Apache, but when I wanted to learn the other styles, which involved rotating, I needed a good, safe, non-lethal ammo so I didn't kill myself or break every window in the neighborhood.  Pine cones filled the bill nicely.  A little tape would prevent them from coming apart when used indoors.  Just a thought.

use a light enough sling that's short enough and ping pong balls fly hard and fast, but loose speed and distance quickly past 15 yards. i've slung them at walls in my garage, their fun to do but bounce a lot.

I thing that better than ping pongs are "anti stress" balls.

http://www.google.com/search?q=anti+stress+ball&hl=en&client=opera&hs=Z2n&rls=pl...

They are pretty light (~20 grams) and soft but big enough to open the pouch of a short and light sling freely. I used to have a great fun with them.