Is there any software which can convert a photograph to a black-and-white outline containing tiny numbers stating which color to give each area?
You could try plainclothes' suggestion, but personally I wouldn't count on Illustrator's live trace producing very usable results. Live trace has its limitations. Even the best live trace algorithms can't make a normal photo into a genuine illustration. When you compare the results from live trace to a hand-drawn illustration, it's quite obvious that today's software just isn't able to create sufficiently subject-aware outlines and color boundaries to produce passable results.
Unless you feed the live trace algorithm an illustration to start with, it's just going to look like a photo that's been put through a live trace filter. And that's not going to make a good paint-by-number outline.
At the end of the day, artists and illustrators still serve a purpose. And to get the desired end product, you'll need to hire a professional illustrator to create a suitable painting/illustration that can be reproduced in paint-by-number style.
If you don't want to spend the money to do that, then your best bet is probably to live trace some stained glass artwork. This is really more color-by-number, but it doesn't require an actual artist to manually create the outlines.