I am trying to create an Apple ID for my child. When I get to the point to verify I'm an adult (enter card)/verification code it gives me the message, "There was an error, please try again later."

This was also happening for me so I phoned Apple Support. You can't use paypal as a method to verify you're an adult, so you need to add a different payment method to your Apple ID (under Settings on your device, Payment & Delivery) and then start the process of creating the child's Apple ID again and select "use a different payment method" when prompted.

Make sure you have entered all the required information as per this article: Create an Apple ID for your child - Apple Support

There's a slight chance something isn't working at Apple's end. Check here --> Apple - Support - System Status

If that doesn't work then for that kind of unspecific message I suggest you contact Apple and ask them what the problem is.

Refer to this document for ways to contact Apple --> Choose your country or region - Official Apple Support

Select your country (also look for "other" regions), then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service by telephone --> Contact Apple for support and service - Apple Support

To be clear:

You first need to establish a family organizer using an Adult’s device.

THEN you create the child’s AppleID.

Follow the directions Limnos provided.

And do provide an accurate birthdate for the child.

Trying to take shortcuts will cause nothing but problems going forward.