One word, Shellac...
Give it a few coats of Shellac as a primer than paint...
The reason I suggest Shellac, is the same reason it's still being used unchanged for 2000+ years now, it simply works... Unlike many other primers it has a greater tendency to soak into the wood beyond the surface creating a real hard candy shell layer that isn't simply sitting on top of the wood...
Also clean up is easy with common household ammonia and soap, can be re-coated in about 15 minutes and for the most part is non-toxic... The only toxic part being the alcohol it's dissolved in, but that isn't really even that toxic, but still use ventilation when using it...