Perhaps give them several different scenarios and ask them to compose an apology appropriate to each one.
For example, a formal apology: They misbehaved in school but their behavior was misinterpreted. Maybe they impulsively kissed a classmate on a dare, and now they are being charged with "sexual harassment." They must write a formal letter to the school administration explaining that their actions were all in fun and not meant to be abusive or harmful.
An informal apology: They accepted an invitation to a friend's birthday party, and for some reason did not attend. They write a note with an explanation (I was sick, my mom wasn't home and couldn't drive me there, my family had to go out of town at the last minute, etc) and a sincere apology for missing the festivities.
A casual apology: One of their school friends suddenly snubs them, and they don't know why. They write a short note to hand to them in class or slip into their locker: "Did I do something to offend you? If so, I apologize...." That sort of thing.
Hope this was of some help.
- For Teachers