There is no single perfect month
Sri Lanka has two monsoon systems. The south and west are generally drier in the northern winter months; the east often behaves differently later in the year. We plan around that, rather than pretending every week is beach weather everywhere.
South coast and Galle
For Galle and Mirissa, travellers often aim for the drier south-west season. A coastal retreat still works in shoulder months if you accept some rain and keep days unhurried.
Hill country
Tea country can be cool and misty in any season. That is part of the point of Ella and the hill-country train. Pack a layer; do not treat the highlands as a beach.
Wildlife
Dry months generally make game viewing easier. Some park blocks close seasonally. Yala versus Udawalawe matters as much as the month. Jeep hire and tickets remain separate unless stated.
Tell us your dates first. A tailor-made plan can emphasise the kinder coast rather than forcing a south-coast beach in the wrong week.