Traveling to Central America with Explore at any time of year is a fascinating experience, and in reality there is no 'best time' to visit the region, as each country differs so massively from top to bottom.
In some countries, like Costa Rica, the different coasts and rainforest areas have different climates even within the same month. On an Explore trip to Costa Rica we tend to see the majority of travelers during December to March, which is commonly seen as the 'Dry Season' in Central America. However, the 'Rainy Season' months of April to July can still be a great time to visit Costa Rica with only showers punctuating the day, and the rest of the time the jungles are beautifully green.
September to early November is often the hurricane season for the Caribbean coast areas of Belize down to Costa Rica, and the weather at this time is often hot and humid. However, that's not to say that it isn't a good time to visit the interiors of these countries.
The Easter period can often be a busy time to visit Central American cities, but very worthwhile to see the colorful festivities particularly in Guatemala.
In sum, a trip to Central America will fit your requirements at any time of year, with a country for every season!