The best way to build your child's credit is to educate him/her in depth about credit, what it means, how it works, and the perils of carrying a balance/maxing out cards/living beyond your means.

The earlier suggestion about adding his/her name to an old, unused account with a good history is a decent one. Another option is to obtain a traditional green American Express CHARGE card, on which you can't carry a balance -- theoretically, it is a good way to build up a credit history.