How are electronic musical greeting cards made?
These sound chips were and still are a creation of Seiko/Epson corporation or one of its subsidiaries.  It was a spin off product from the extremely low power CMOS processes that they developed for the watch business.  The design of the IC itself is actually a 4bit uProcessor with mask ROM for the different "tunes". They also provided more expensive OTP (EEPRom) based units for experimentation before changing the mask. 

I'm sure that there are a number of companies that could make these and searches on "greeting card music chip" show lots of Shenzhen references.

They are purchased as KGD (Known Good Die) in waffle packs and then glued to the PWB (PCB), wired bonded to the pads and covered with epoxy.  I'm sure now a days you could get them with bump bonds.