Q: What do you do when your manager has a negative attitude? It ends up affecting everyone in the department.
A: Talk to your manager, and, in a subtle way, tell him he is being negative. Let him know that his moods have a dramatic impact on everyone in the department. "Because you're the boss, we're very sensitive to how you feel" would be one way of saying it.
Don't worry about the repercussions. After all, most bosses love attention, and this gives them attention. They probably know something is wrong, but can't figure out what it is. If you do this discreetly and diplomatically, he will appreciate it, even though he may not admit it.
You could also practice behavior modification by reinforcing any positive things he does. Encourage the good, try to ignore the bad. Look at it as an experiment. Give yourself some scientific detachment and see if there are things you can do to reinforce the behavior you want.
And, above all, don't let him influence you. Maintain your own positive attitude and support your colleagues. Help steer the department in the right direction and keep everyone's moods upbeat.
This will serve you well in this and/or any future job you may have.