Depressing, yet somehow optimistic. Typically used when something bad has happened and a pathetic attempt is made to be optimistic about it. It often leads to feeling more depressed.
This would be depressingly optimistic:
Someone you've had a crush on that you couldn't work up the nerve to talk to dies. Trying to be optimistic, you tell yourself, "Well, at least I don't have to stress over trying to ask her out.". Depression sets in when you realize how much you wanted to try.