I'll let Chris give the official answer but here's my suggestion.

Call the hotel and let the manager know what you're planning. As long as they can get credit from Marriott for the coupon, they should be happy to let you use it. If Marriott requires the hotel to physically receive the coupon and related payment (for the other night) before January 1, 2005, simply offer to pay for your stay when you check in, rather than when you check out. The hotel gets the cert before it expires and everyone is happy.