You may want to check out the singles area here, there may be something about this. The only problem I can see is with booking a cabin, you will probibaly have to pay a full fare for your son, unless there is some special share thing you can find. In the meantime, I'd suggest giving a travel agent a call and see what they can do for you. Here is a link to the singles that may help:
Absolutely, you'll find single parents with a child -- I once sat at a table aboard a ship with a mother and her daughter, both having a ball. You'll find grandparents with children and any possible combination of family members. Cruising is the best deal around -- you pay 80% of your vacation costs up front. Your food and entertainment, on-board kids programs, are all included in the fare of the cruise. Carnival has large cabins, very reasonable rates and terrific kids programs -- personally, I'd go with them. They also carry more singles than any other cruise line.
I suggest you find a good agent with experience in cruises. The "classified" area of CruiseMates is a good place to start calling. I believe airlines and cruise lines ask for a letter from your ex saying it's ok for your child to go with you, but check this out with the agent. It's their attempts to help stop kidnappings.