I've looked at zero-VOC interior paints and the like, but without a great deal of success. There seems to be a lot of focus on environmentally-friendly paints in the EU, but that hasn't translated to a lot of available products in the U.S., and even those in the EU don't appear to be rated for use on toys (or often even wood.)
I have tried milk paint (also available on Amazon) and I like the results, with a couple of caveats: it is not cheap, at all, and you'll definitely wind up on the "rustic" end of the spectrum of colors and effects. I ordered the full sample pack for $52, which is rather a lot of money for rather a small amount of paint, and I've tried three of the colors so far. It's fairly simple to control the dilution (if not the stubborn clumps of powder) - I just winged it with some water and powder and a cheap brush. After it was dry I sanded it back down with a scrubby and sealed it with beeswax polish. I'll use it again.
Paul Greve sent me some great photos of the terrific toys he paints using milk paints:
While I'd love to try this, it is prohibitively expensive, at $12 for a half pint of one color! They also don't say anything on the site about using it on wood or for toys, so it probably isn't certified or approved. For the wealthy out there, you can find it here.
I know of at least one toymaker who makes and sells his toys using Do It Best (made by Rustoleum - possibly not anymore) Latex Enamel. This is supposed to be non-toxic once cured but I personally think that it seems a little heavy on the chemicals to make it really safe for toys.
A visitor emailed me to ask about using Flour Paint, and I have not tried it. It looks interesting, but I wonder if the ratios would work at smaller quantities - there's various boiling of things like linseed oil involved. Additionally, it's important to note that this paint is only as non-toxic as the pigments you choose. Some pigments can be incredibly toxic and some completely benign - so it's important for you to research your pigments as well as your recipe.