I'm the family cruise editor here at CruiseMates.com. While I haven't cruised to Belize and Honduras, I'm sure there are great beaches there that your child will enjoy. I find that toddlers and pre-schoolers do best at the beach anyway, rather than on a guided tour. Ask the shore excursions personnel to recommend a beach that you can reach by cab and that have bathroom facilities.
I have been on the NCL Sun and it has a nice, large kids' room. NCL's youth program has been lowered this year to include children age 2 and over, so your little one should have plenty of company his age. Note that if your son isn't potty trained yet, that the counselors will give you a beeper and page you if a diaper needs changing. They don't change diapers themselves.
We took our daughter four years ago on NCL when she was four years old and she had a great time. The counselors were very warm and even though the youth facilities were not as nice as those on the NCL Sun, she still had a memorable cruise.
Luisa Frey Gaynor