Speaking from the other side... I'm a unipolar depressive, I don't have the manic side. My "mood swings" are not as significant, sometimes there are none. I was never a boy for sure, LOL but I was a young depressive and now an old depressive. LOL
There's no one good answer. All of the above are good for one time or another. What you're feeling is what you're going to feel, frustrated, sad. And he needs to know that you feel that, that you love him, that you'd do anything for him, etc. But bottom line is that he has an illness. His hormones, brain, whatever is causing this. He can't change that but he can learn to understand it so he learns how to live with it.
Main thing you need to know is that he sees nothing good. It's like a total eclipse. He sees no hope, no improvement in his life. So one thing you need to do for sure is to talk about good things in the future. Being a kid those need to be in the immediate future, next weekend, school event, play date with friends, etc. Set up something immediately if necessary. Talk about a movie he wants to see, video game he wants to play and rent it. Keep him with someone at all times. Worry about suicide. But also, depression, hopelessness includes loneliness. So bake cookies with him, play a board game, whatever you can get him to do.
Get him in some kind of support group so he knows he's not alone, doesn't feel like he's weird.
Keep his environment and everyone around him positive, cheerful. I walked into a potential class for my child one time and observed for a half hour. The teacher didn't smile once in that time. Found out later she had recently had a terrible trajedy in her family so it's understandable. But not good for a child vulnerable to depression. If he has friends whose parents have recently separated, are seriously ill, etc spending a lot of time with negativity will bring him down. Being depressed it will also give him something negative to focus on when he naturally is looking for something negative. Make sure he gets sun, with sun screen obviously. But SAD can contribute. Since you're where you are, if that's a problem, look into putting the kind of light in his room that helps with SAD. But lots of light in the house is important. Also color, be sure that the colors around him, the whole house, are cheerful. Bright pinks seem to help me but I don't know about little boys.
Exercise is also important. Lots of studies on that. Must exercise regularly for as long as possible. So family walks or bike rides helpful.
Most important thing is that he learns to be aware of his moods. He needs to learn to look for logic and reason to overcome the negative thoughts. He needs first to learn to recognize negative thoughts and thought patterns. It's much more subtle than it might seem at first. If someone passes him on the street without looking at him he might assume that it's his fault. Chronic blaming himself is very, very common.
There's a book I always recommend that parents read with their kids. It's kind of an introduction to therapy for kids. I'll dig up the name. He needs to be in therapy for many years in front of him. It's never too early to start.
One other subtle thing... give him positive statements, congratulations, affirmation, etc all the time, ALL the time. Leave him notes telling him you're proud of him for doing xyz, talk to your friends in front of him about how great he is, kind, compassionate, etc, etc. It should be things that he consciously did so that it's reward for his effort. False praise not helpful.
Remember that the tears are a symptom of pain. It's not pain you can cure with an aspirin but it can feel like physical pain. Chronic small illnesses are a common sign of depression. The illnesses are real, but they go away when the depression does. So do what you would when your child is in pain, hug him, hold him, let him sleep with you, lots of TLC.