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I'm not sure what genre you're looking for. But here is my list. None of these are new and most are the rock/alternative genre.
What I listened to a lot when I was depressed was Three Days Grace. I think a lot of their songs are about depression, but mostly "One-x", "never too late", "life starts now", "world so cold".
These might not be about depression per say, but there's also Pink's "Fuckin Perfect" and "Sober" and Seether's "Fine Again" and "Rise above this" and I feel oftentimes like Sick Puppies "Odd One" and can relate to Garbage's "I'm only happy when it rains"
And in the 90's there's also Blind Melon's "No Rain" Soul Asylum's "Runaway Train".
REM's "Everybody Hurts" is about depression I believe, but I'd opt to listen to their "Shiny Happy People" so I didn't off myself.
These are all I can think about right now.I hope I wasn't too far off the mark. Hopefully others will make better suggestions.