The South Asian part of the AskHistorians book list is essentially limited to subcontinent-wide overviews, or specific events dating to the colonial period and in the north of India.
What are some good books to read if I'm specifically interested in Sri Lanka and South India - in particular the Dravidian-speaking parts of India? I'm interested in anything related to the region, of any temporal or regional scope. I'd be equally happy to read anything from a good regional overview, to a detailed history of Anuradhapura, to an in-depth study of caste in southern Kerala in the early 20th century.
K. M. DeSilva's exhaustive History of Sri Lanka is a great start for all things Sri Lankan. The most recent edition includes a somewhat in depth look at historic Tamil Sinhalese relations and surveys into society and caste in various kingdoms. As for Kerala, I really don't have much background, Oxford published a History of South India ten or so years ago which I've used in the past, but I'm afraid I don't remember the writer, but there was a fairly in depth look a Dravidian culture pre-colonialism. I don't think it goes past the 18th century though.
More of course can be added, but do check out our booklist!