The dry season (November to April) is the most comfortable time to visit Livingston — the Caribbean coast gets serious rain from May through October, which can make the Siete Altares walk muddy and the sea choppy for boat trips.
November is particularly good: the dry season is beginning, Garífuna Settlement Day (November 19) is one of the liveliest festivals of the year, and the tourist crowds are manageable. December through March is peak season — expect more visitors and slightly higher accommodation prices.