How do I record an American Express payment made online not hooked up to bank account in QuickBooks?

Choose the bank account that the payment was made from while recording a vendor check or an expense. Choose for detail the AmEx credit card liability account that contains all the activity in this AmEx account that you previously entered charges to (using expense screen).

If you used an account that you do not track in QB then it is probably a personal account and as such the money provided to pay AmEx comes from Owner Equity Contribution. You cannot record a check or expense from an equity account so you will have to set up a dummy clearing account (bank type) to not only receive a deposit from owner contribution but also to pay AmEx