You may be able to restrict calls to the numbers in the phone's contact list. Some phones do this and some do not.
If your phone has this feature it will be under the security options. These are usually under the Tools and Settings menu. To change the security options you will need to know the phone's security code. Unless you or your child have changed the security code it is the last four (4) numbers of the phone's phone number.
When you enter numbers in the contact list be sure to enter the entire 10-digit number. This will help to ensure that your child can call those numbers without any problems.