For the US market, there's at least one company that provides this data. Unfortunately, I can't remember the name, sorry. :(

I do know it exists, though. I used to work for a major American tire manufacturer and maintained a couple of versions of their tire selector application. They would send over a huge file (I think a spreadsheet) with a combination of every year/make/model/trim and its associated OEM tire sizes. I think we also sent over a list of our tires (models and sizes) and they would include that in the db for us. I believe it was left to us to import and normalize it, which was kind of a pain in its own right.

Car make / model - there's only a finite set of these. Take a look at the categories on Autotrader or something similar. Tire Sizes - ask your local mechanic how they would find this out? There's probably a catalogue they would use.