Looking Up at the Half-Moon
半分の月がのぼる空 (original)
A hospitalized teenage boy befriends a young woman who also suffers from a health issue. Despite their ailments, they form a lasting romantic bond.
Starring Nobuyuki Kobushi, Kenichi Suzumura, Mikako Takahashi, Kōji Yada, Yuuki Kodaira, Hiroaki Hirata, Akira Sasanuma, Yuki Matsuoka, Miyu Matsuki, Sanae Kobayashi
Watch "Looking Up at the Half-Moon" on Tubi TV released in 2006. It's a animation and drama show, and has a rating of 7 out of 10 from Imdb which is usually fine for this kind of show, and is currently available to watch for free.