Tamil romance is a whole mood online these days, but finding the good stuff can be a bit of a scavenger hunt depending on whether you're looking for traditional novels or web originals. For physical books, Google Play Books has been my most reliable bet—they have a solid collection of ebooks from established Tamil publishers. You can find authors like Sujatha and Balakumaran there, and the translations of popular romance from other languages into Tamil are also well-represented. The search function is decent, and previews help you decide.
If you're into the serialized, modern stuff, you might have better luck on platforms that host Tamil web novels. I've heard of sites like Thannambikkai and iStory, though their interfaces can be a bit clunky. They often feature love stories by upcoming writers, some with a very contemporary, urban feel. The quality varies wildly, from surprisingly poignant to... well, not so much. It's a bit of a gamble, but that's part of the fun sometimes.
A lot of readers I know actually turn to YouTube. Seriously. There are channels dedicated to narrating full Tamil romance novels in audiobook format. It's perfect for listening while doing chores. The narrators add their own dramatic flair, which either makes it better or hilariously over-the-top. Finding popular titles this way is easy—just check which videos have the most views. It's not a 'reading' experience in the traditional sense, but it's how a lot of content is being consumed now. I found a channel that did a fantastic serialized reading of a novel called 'Kadal', and I was hooked for weeks.