There is a link on the DCL website to make a payment for an existing reservation. I've never booked a cruise there, but I would expect that you could pay a deposit of anywhere from the minimum up to the total cost of the cruise when booking.
If a discount does become available, I think you'd have to call the line to see if can be applied to your reservation. There is no option to alter a reservation, at least not that I can see.
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