>Wouldn't that chip?

It should not chip if applied correctly (very thin layer(s)).

>What kind of paint would you use on plastic like this?

Well, personally I wouldn't! I think black buttons would be even harder to find/use at night. But were I to do it, I'd start with whatever scrap paint I have around the house -- way too wasteful to buy a new can just for four itty bitty buttons, unless I had none.

So, I'd pop out the buttons, scuff lightly with 240 grit sandpaper, and wipe on some acrylic primer. A few hours later, I'd wipe on a very thin layer of black acrylic, and tidy up any bald spots with a second coat the next day. Finally, I'd give it a thin spray of acrylic sealer (either matte or glossy) if I could find my can of the stuff.

Cheers