Humorous speaking does not mean telling a series of jokes.
You can make a point through exaggeration [If I've told you once, I've told you a thousand times, don't exaggerate].
Ambiguity or puns can add laughter: [The duke reported that the peasants were revolting. I know said the czar, but they are own people.]
Using an accent is something that I suggest that you only do if you can do it very well, but once you do perfect the technique then it can create a pleasant surprise
Drama and pathos also create a bond between the speaker and the audience. If you are involved in a story that has a surprise, but unpleasant ending, provided that you have learnt a lesson from it, then the audience will emphasise.