When my son was little, we occupied him with a kid size fishing rod so he could occupy himself. We also allowed him to "sail" the boat (with adult hands on the wheel, of course) and it made him feel like one of the big guys. Since it looks like you'll be on a cat, puzzles and board games would probably be a good idea, provided someone is willing to hang with him! It would be tough to do that on your Hunter since every time you tacked, all the hotels would slide off of Boardwalk! Maybe the adults could put together a "watch schedule" for when he's awake so he and the adults get some variety and no one feels overly obligated to be primarily responsible. Our big thing with our older daughters (they were 14 when he was 2) was not to make them the permanent babysitters. We also always wanted to (and still do) buy one of those collapsible "net pools" to deploy at anchor that keeps them corralled. And of course, if something goes wrong aloft, he is the lightest!!!
Until Sean was 5 or so, as soon as the sails went up, he drifted off to sleep so we didn't have to occupy him the entire time. Now that he's older (8) he has his iPod and DS to pass time. He does steer (we are next to him the whole time but he has the wheel) and help out with sail trim. He still fishes, and once in a while he serves as "navigator" by checking the charts and keeping a look-out. He actually had my captain's books out last night and was brushing up on ATONs and piloting navigation to get ready for spring.
Good luck and have a great trip! Post some pics!