I found two sites that you can find them online.
Tamil books online. PDF Tamil ebooks for download | Tamilcube
தமிழ்காரன்: Free online Tamil Books Library
Where can I get the Tamil story books Online?
Hello ,you find perfect Tamil story book online on different site like, amazon.com,flipkart.com,snapdeal.com, askmebazar.com .
Wattpad maybe the are many free online books there