Try fill the billing address with your relative's. If that does not work (likely), call Costo.com customer service then they should be able to figiure it out. The problem is not that Costco.com does not allow Canadian billing address. It is the automated credit card billing system will check if the billing address in your credit card's record matches the one you provide online (at Costco.com). So if the the dumb computer cannot figure it out (i.e., cannot authenticate the transtraction), a human operator should be able to find a way to fill your order.
Good luck!