You can try this website :

https://giovanni.gsfc.nasa.gov/giovanni/

Important: CSV data are also available.

You can contact the Meteorological Department of Sri Lanka.

Dont you have any weather station!

Regards for all supports

https://chrsdata.eng.uci.edu/

We can download it from the above URL

Meteorological department has data in digital format. When I obtained data ~10 years ago, I had to pay for digital data. I could copy the data from their logbooks free of charge. Alternatively, you can look for satellite and model based global rainfall products (e.g., TRMM, PERSIANN). But, these products have a coarse spatial resolution and the accuracy might be low.