The dry season coincides with holidays in Europe and the US, which increases tourist flow to Honduras. It's a good time to visit the Caribbean coast and the islands as it is less rainy. Also, sunny days are perfect to visit Mayan archaeological site like Copán and hike in the mountains, although it can get chilly there at night.
On the mainland the peak season lasts from January to June and at the Bay Islands it's September. Weather and water temperature in Honduras in these months are excellent. The sea can get very warm, up to + 27°C and higher. This season is the most convenient for water activities, as well as whale shark watching. Don't forget that the weeks around Easter, as well as Christmas, New Years, and Thanksgiving are when the cruise ships start visiting and are considered to be the busiest times in Honduras.