The birds largely decide it, but the other elements have their own seasons.
December to February is the best all-round window — flamingos at peak, comfortable at 24–29°C, and the lagoon at its most active.
November brings the northeast monsoon and this coast catches it directly. Cyclone risk is real. The birds are arriving but conditions can be difficult.
March to May is hot and humid. Flamingos have largely gone, but Nagalapuram is at its best — the trek is more comfortable in warm weather since you are wet throughout, and the pools are inviting.
June to October is quiet and cheap, with resident birdlife rather than migrants. The Nagalapuram trek may be closed after heavy rain.
If flamingos are why you are coming, travel in January. If the trek is the draw, March or April.