101 Marriage Proposal is the third Japanese drama title I had watched. It aired in 1991 making it almost 2 decades old. I have not watched the drama again ever since, but I still remember it as very touching.
Synopsis from DramaWiki:
101st Marriage Proposal is a “Beauty and the Beast” story starring Takeda Tetsuya (Virgin Road, 3-nen B-gumi Kinpachi Sensei) as a down-on-his-luck man who has gone through 99 omiai (arranged dates with the intention of marriage if the date goes well). Not particularly smart, nor handsome, nor rich, he is a man who cannot lie and of course, has a heart of pure gold. On the 100th omiai, he meets Kaoru (Asano Atsuko), an extremely beautiful and talented cellist who can’t forget her dead fiancee.