Contact your travel agent or the cruise line directly as soon as you need to add another passenger to your cabin. Explain the situation to them.
If you are adding a passenger to a cabin that can accommodate three or four people, there shouldn't be a problem. The biggest issue is if the ship has already reached its sailing capacity. So the earlier you book, the better.
If you try to add another passenger to your cabin after you've requested a "single" accommodation, you'll need to upgrade to a larger cabin or to a suite. The extra cost will vary, depending on the cruise line.
Book a "Handicapped Cabin" for your cruise in advance and you won't be able to add an additional passenger, unless they too are handicapped. These cabins are reserved for passengers with disabilities only.
Make the reservation for the extra passenger, then arrange to pay the deposit for their fare.
Consider canceling the cruise and rebooking it for a later date if you're unable to add a passenger to your cabin.