Interesting.
I know of no song or piece of music that I find 'depressing' at all, although loads of songs and instrumentals make me cry where ever i am - in the car, at home, what ever.
I don't think Leonard Cohen is depressing at all, he is wry and melancholy.
The first time I heard 'Tears In Heaven' was before it was released. Eric Clapton was on TV talking to Sue Lawley about the son he had just lost, and then he played the song live with an acoustic, and I howled!
I recall friends talking about Harvey Andrews supporting Focus on tour in the 1970's, and when he sang The Soldier, everyone in the hall was weeping by the end. When he returned, and everyone knew what he was going to sing, they cried as he started the song! Remember, the 'troubles' were at their height, and unemployment was rife, making an army career seem like a god options.
Isn't music fabulous - to connect us with our emmotions like that?