How do I change the Apple ID to a different email address for my child?

If he has his own Apple ID, note the restrictions in the article.

Apple ID Name Change.  * 

 What to do after you change your Apple ID or password - Apple Support  *  I suggest doing this before you change your Apple ID or password.

This depends on what you wish to achieve, which you haven't stated. By "change" and "different" do you mean that your child already has an Apple ID email address or uses yours?

There are a few options depending on how or if you want to monitor your child's email - and this may depend on your child's age.

1. You could create a new Apple ID
2. You could create an email alias for your child from your account - although this would also appear in your In and Sent email boxes.
3. You could create an email alias for your child's existing account