But humor and seriousness themselves work along several axes. For example, does the humor work through exaggeration or through understatement? Is it cruel or compassionate? Is it merely whimsical or does it have serious intention behind it? It might be "gallows humor" or cutting irreverence, or grotesquery. It could be absurdism, Beckett style, or Kafkaesque humor, or Kenneth Koch style parody.
Does the humor expand into exuberance, Kenneth Koch style, or does it lead to narrowed, embittered world-view, a la Philip Larkin? Does it begin in pessimism, as in Beckett, but with the possibility of unexpected moments of joy? "Hope is a thing with feathers" is kind of a funny line (Emily D.). Is it funny in the same way as Byron? Probably not. You could tell a bad joke, knowing it's bad, or say something funny that people aren't quite sure is a joke or not.
Much humor derives from incongruity, like irony does, so humor and irony have common sources. But suppose we notice an incongruity or disparity, aren't there many possible attitudes we might adopt in relation to it? So irony is not a single attitude, but an opportunity for diverse attitudes to come into existence.
If it is a serious attitude, does the poet tell you why? Is it justified? If he or she is being solemn about something that is not earth-shaking in its consequences, then that could be unintentional humor. How much self-awareness or self-indulgence is there? Where does the authority of the poetic voice come from? Does the tone match the formal and sonic qualities of the text? For example, a solemn limerick might not work very well.