There is no dress code specific to children; just follow the same guidelines for them that you would for yourself. For smart casual just wear what you would to a nice restaurant at home. No shorts, Ts or flip-flops at dinner (they are okay at breakfast and lunch). On formal night a tie and jacket might be nice for your son, but is not required.
During the day jeans and sneakers are certainly allowed; but it is going to be hot and I'm sure they would be much more comfortable in shorts and flip-flops. Chances are they will be in bathing suites all day.