I remember a while ago there was a thread about how adults could call in sick to work, but kids didn't have that option.
However, I discovered (accidentally) while playing that you can, in fact, keep your child home from school when sick! As long as the kid has the 2-day "Germy" moodlet, you will receive a message saying something along the lines of: "Thank you for your consideration in keeping your sick child home from school."
He or she will then be unable to go to school for a day, much like when there's a holiday. In other words: Townie DecaDynasties, watch out.