You can Write Tamil letters For free online without installing any Tamil keyboard softwares
www.quillpad.in/tamil/ -this website is also offering the same kind of Tamil Tool to write Tamil letters. using the free language conversion tool you can use any keyboard to type letters in tamil, no installation required.
Ok, How to Type Tamil Texts on Facebook?.. There is video in youtube where we have shown this tool demo to know How to Type Texts in Tamil on Facebook and Twitter.