The Toyota Service and Repair Manual (TSRM) for the Supra is the best manual I've found. There is a digitized version hosted online for a '90, most of the differences are electrical though so it'll be fine for your needs. I recommend buying a hard copy though... a LOT easier to flip through while you're in the middle of the job. It's not the cheapest publication out there, but it's much better than Haynes.
Online version:
http://www.cygnusx1.net/Supra/Library/TSRM/MK3/ (You need the Engine Mechanical section
)