Jeff Buckley, although he doesn’t make me sad as much as he makes me think he is theatrically wallowing in despair. Nick Drake is a good choice. So is Tori Amos, which is why I don’t listen to her so much nowadays.
I’m still mad at him for that time he framed Krusty the Klown for armed robbery.
Jim Morrison of the doors.
Add his voice to the countless cheesy chords played by Ray Manzarek and I start stabbing my ears with pencils.
Paul Simon. Talk about a Gloomy Gus. I can enjoy the music and wordplay regardless, but Mrs. Cretin can’t take much of him. “He’s a downer, man” she says in her best Tommy Chong voice.
Tom Jones brought out a song last year that was so depressing, he should have been shot for doing it.
Don’t blame Tom, that’s a Leonard Cohen song. Another gloomy Gus, but he never depresses me. He has a sense of humor and his words are just too exquisite.
Johnny Ray. 
Karen Carpenter. I absolutely love her voice but it is haunting and depressing even for some of the more upbeat tunes. The fact that she died slowly and tragically from anorexia doesn’t help matters.
Leonard Cohen
Basically the whole album is hard for me to listen to, even though she has a great voice.
Marianne Faithfull. It’s the delivery, not even what she sings about.
(And I get sad when listening to some Stan Rogers because I miss what he could have done, but it’s not depressing.)
Sandy Denny. There seemed to be so much sadness in her songs, and she left us too soon.
The Eels. The lead singer’s life got all fucked up about the time his band got famous.
Billie Holiday makes me sad, content, and then sad again.
Billie Holiday is our heroin, and heroin was Billie Holiday’s heroin. 
Tori Amos
My dad died two or three months after Croce died, and my dad really liked “Bad Bad Leroy Brown” and “You Don’t Mess Around With Jim”. “Time In A Bottle” brings me to my knees, albeit not quite as devastatingly as it used to but…um, yeah.
Poor old Johnnie Ray. Sounded sad upon the radio. Moved a million hearts in mono.
Harry Chapin.
Amy Lee of Evanescence, especially “My Immortal.”
Lock up your razor blades before listening to The Shortest Story.