Sri Lanka has two monsoons on opposite schedules, which is the single most useful fact about visiting it.
Most people asking about the monsoon are picturing a European idea of rain: days of grey drizzle that cancel everything. That is not what happens here. Monsoon rain tends to arrive hard, in the afternoon, and be gone within the hour, and the light either side of it is the best light of the year.
Two coasts, two seasons
The southwest monsoon soaks the west and south from roughly May to September. The northeast monsoon does the same to the east and north from about November to February. They do not overlap, so at any point in the year one side of a small island is dry. Planning around that is most of the work.
What we change, rather than cancel
Beach days move to the coast that is having its summer. Park days move to the early morning, which is when the animals are out regardless. Long drives move to the wettest afternoon of the week rather than the clearest. Almost nothing needs to be cut; it needs to be reordered.
The upside nobody mentions
The waterfalls are at full volume, the hill country is green rather than scorched, the parks are quiet, and the rooms that cost the most in February are half of that. If you can tolerate an hour of rain a day, the shoulder months are the best value on the island.