The two-monsoon rule
Sri Lanka has two opposing monsoons, so somewhere on the island is always in season. The south-west monsoon ("Yala", roughly May to September) soaks the west and south coasts and the hill country; the north-east monsoon ("Maha", roughly December to February) brings rain to the east and north. The practical upshot: you move coasts with the calendar rather than picking one "best" month for the whole island.
December to April is generally best for the south/west coast and the hill country. May to September flips to the east coast, when Arugam Bay's surf peaks and Trincomalee/Nilaveli are calm and dry.
Best season by region
Season guidance is general climate advice, not a guarantee, shoulder months can work well on either coast with the occasional shower.