Follow the instructions in this support article to create an Apple ID for your child - Create an Apple Account for your child - Apple Support
To me it is sounding like you have somehow already used the email address with Apple.
Change your Apple Account primary email address - Apple Support
- If you remove an email address from your Apple Account, it can’t be associated with another Apple Account for 30 days for security reasons.
If you can’t change your Apple Account primary email address
- If you try to change your Apple Account to an @icloud.com email address that was created within the last 30 days, you will be asked to try again later.
- If you see a message that the email address you want to use isn’t available or is already in use, check that you or a family member aren’t already using that email address with a different Apple Account. If a family member is using that email address, remove it from their account, then try to use it.