While I would never condone credit card fraud, if the child's last name is the same as an adult (parent or otherwise) with a valid credit card, I may have found entering the child's first name with that matching last name with the rest of the valid credit card info seems to work....

Meaning the "name" field in the credit card billing info must match the AAdvantage account, but the first name of the credit card info does not need to be correct for the billing to go through (at least with one credit card I might have).

Just a thought, and of course, YMMV.