I would assume that a down payment could not be paid for via an AmEx the reason I say that is most lenders I've ever dealt with want "seasoned" funds for the down payment. Seasoned are funds that have been in your personal account for a period of time or equity from a home sale.
Besides the mortgage company requirements there is the attorney or closing agent who will need funds to complete the transaction. You would need to pay the down payment many days in advance and probably pay the fees. I've never seen an agent take any cards debit or credit for the down payment or another fees at a closing.
I understand why you'd want to do this and I'd love to also hopefully someone has a way.