I like the idea of a security question, though in a playground situation 'what is your favourite colour' is sucepible to brute force attacks, and 'who is your favourite band' would have a short expiry time. I've noticed that online banks and the like will often ask you several security questions, and ask you a random one though, which might suit your needs.
in reply to Yes, Passwords...but...
Alternatively, scenario-dependant, you can either produce a teachers control panel where the teacher can log in, and click a name from a list for a new one (if it's for a classroom environment) or issue each parent with a password that will reset their childs password.
Have you considered 'something you have' as a method rather than 'something you know' (I'm guessing that 'something you are' is a bit out of your budget) give them long, cryptic passwords, printed on a label on a keyring. That way they can get it when they need it, and yet should still take good care of it.
Though knowing kids today, you could just use SecurID with software on their mobile phone.