Different parts of the country receive rain at different times of the year. The center, south, and west of the country tends to have rain from around May to July and also from October to November. The north and west typically sees rain from December to February. That said, I've noticed that the rainy season has become less and less predictable over the last several years.

Re: newspapers - "The Morning" (http://www.themorning.lk/) is probably the daily with the best online presence. The Sunday Times is decent as well (http://www.sundaytimes.lk/ - click on the "print edition" link in the header to access the detailed version).