I guess White Christmas could be considered but it's kind of a stretch.
All I could recall were movies but if you're still interested: When I Kill Myself, Solomon's Perjury, Kiss Me Kill me
In Angry Mom, part ofthe plot is about the suicide of the daughter's friend/classmate. It's not centered on suicide, it's more about bullying. It's quite a serious drama (it's tagged as "comedy" and it has comedic elements to it, but it's primarily really a serious drama).


Suicidal people as protagonist:
Ashita no Kita Yoshio
Haitatsu Saretai Watashitachi
Arifureta Kiseki

I think teenage angst dramas like Hormones and School 2013 has suicide subplot too.
thank you all for your replies :)