Does your debit card have a Visa or Mastercard logo? If it does then it should work, but I really don't know because I've never ordered from Coach.com before. If you have access to a boutique you should order there anyway so you get free shipping.
^ They do I Canada. All of the debit cards are tied to your bank account and not affiliated with Visa or MC in any way. When I go to the States to shop my debit card is not generaly compatable with the sytem that the store is running.