I keep getting a network error message when creating an account for my child.

Hello nelia113,

Thank you for using Apple Support Communities. Sounds like you're receiving some network error messages when trying to create an Apple ID. If so, we'd like to recommend some steps to help you isolate this issue further. Let's follow the steps below:

1.) Connect to a reliable Wi-Fi network. If you're already using a Wi-Fi network, you can try connecting to a different one to see if that helps with your network error.

2.) If you're using your iPhone, try using a computer to create the Apple ID. Use the article viewed before posting for these steps also. Here is the link again: Create an Apple ID for your child - Apple Support

In macOS Ventura or later

1. Choose Apple menu  > System Settings, then click Family. 

2. Click Add Member.

3. Click Create Child Account.

4. Follow the onscreen instructions to finish setting up the account. Be sure to enter the correct birth date — you can't change it later. For your child's Apple ID, you can use their email address or their Game Center nickname. 

If you don't have access to a computer you can use and you continue to receive network errors while trying to use your iPhone, you can try to reset your network settings. Tap Settings > General > Transfer or Reset iPhone > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you’ve used before. If you're using iCloud Keychain, these settings are also removed from other signed-in devices.

Your iPhone will restart during this reset. After it does, reconnect to your Wi-Fi and try again. We hope these steps help you out. Thank you for using Apple Support Communities. Take care.