If this year is typical, you can expect brief (20 to 30 minutes) of very heavy rainstorms, particularly in the afternoons. I have dove Bocas in mid-May and we had a few heavy rainstorms. I don't know what it takes to ruin diving for you, but you can still see a lot of interesting, unique fish and beautiful coral while the rain is pelting the surface. Fortunately, it's Panama, so it's a warm rain. However, you might want to have a windbreaker for the boat ride back to the shop.
In June 2007, July 2008 and May 2009, my wife and I dove at Portobelo and didn't get a drop of rain. (The visibility was nice, too.) A few days on either end of when we were diving could have been totally different. For that matter, at any time in Panama there can be rain. As my good Panamanian friend Joaquín says, "There are two kinds of weather in Panama; rain or no rain. And, there are two seasons; hot or nice."
As for your son, Bocas is just as good or just as bad as anywhere else in Panama. It's going to be very warm and extremely humid no matter where you are on either coast. Keep that in mind and be prepared to fight diaper rash. The food and water are safe all over the country. I would recommend talking with your doctor about things like sun block and insect repellent. While malaria and dengue fever are rare in Bocas, Portobelo, the ex-Canal Zone and Panama City, it is something that should be considered with one so young. Also, if you're thinking about flying to Bocas, the regional turboprops can be rough on a little guy's ears.
I don't mean to sound like a doomsayer, but if you embark on the trip prepared, you and your son will probably have a wonderful time. Buen viaje.
