2 years ago I would say it is impossible. Now I think it is possible. I didn't try it though.

Here is a link that might be useful: household compost

You definitely need air holes for aerobic decomposition which is less smelly than anaerobic.
A worm bin with red wiggler worms might work well with rabbit manure and coffee grounds mixed with paper. Egg shells, fruit and veggie scraps can go in too.
A worm bin doesn't need to be turned. I layer mine and let it sit till it's done. The vermicomposting forum has lots of info on worm composting.
Good luck

So if I want to go aerobic, then frequent turning once (or twice) a week would not be sufficient relative to drilling holes?

And thanks for the heads up on worm composting, I just realized that I might be able to put a bin in my bathroom (I have a badly laid out apartment where the kitchen is really small and the bathroom quite large), so I'll be looking around there...

You definitely need air holes for aerobic decomposition which is less smelly than anaerobic.

Is it really so?
I suspect that bad odours go out from compost by air holes. That is why it is "less smelly". No problem in the garden with this but a big problem on balcony. You'll feel it quickly.

Composting on Balcony is exotic and must be done very carefully. Eliminating of odours is main problem. And most difficult. But it is possible.