Thanks for the suggestions! Here are mine.
Sentenced - Excuse Me While I Kill Myself
Sentenced - Suicider
Sentenced - Farewell
Sentenced - Noose
Sentenced - Bleed
Sentenced - Cross My Heart and Hope To Die
It's an old band (1990s), but I haven't heard of them until recently, all of their songs seem to be about suicide, or at least all of the ones that I liked.
It's ''soft'' metal (melodic death metal).
There's also:
Korn - Alone I Break
Neil Young - Dreamin' man
REM - Everybody Hurts
Megadeth - A Tout Le Monde
Here is a list of songs about suicide, my estimate is that there is at least 500 songs about suicide here.
http://en.wikipedia.org/wiki/List_of_songs_about_suicide