Persuasive essays are fun as they often allow for a bit of humor. Write up an essay persuading your favorite movie star, rock musician or other entertainer to go on a date. Remember to detail reasons why it would benefit them to do so, too. Explain to the celebrity why "money isn't everything," for example. Writers often elevate the sense of humor in their work by using sarcasm. Lay it on "thick," detailing why every physical or emotional failing you have is actually an attribute that simply cannot be ignored any longer.
A fun idea for a persuasive essay could entail that you take on an alternate persona and perspective. You can even take that particular perspective and turn it on its proverbial "ear" with a counter perspective. Galileo Galilei once told people the world wasn't flat, for example. Write a fun persuasive essay as an imaginary beer-chugging member of the Hell's Angels biker gang explaining why the world is, in fact, flat. Consider revising this somewhat to fit other scenarios as well.
Negative experiences are often fun to write about. For example, if you've ever been to a Thanksgiving Day dinner with drunken elderly relatives, you might have something to offer in this respect. Draft an essay persuading an audience why your Great Aunt Helen should be given a prize for pontificating about religion at every given opportunity -- label the imaginary trophy as the "Great Pontificator" award. If you don't have a Great Aunt Helen-like relative, reconfigure the essay with a political figure.
Explain to an audience why your favorite hero is better than any other. You can do this with evil "bad guys" if you prefer. When you write a persuasive essay, be sure to incorporate at least three reasons why your character might prevail in some imaginary battle for supremacy, for example. Teachers sometimes have students use literary characters in a similar manner -- it helps them gauge whether or not a student has read a novel or assignment.