Found a couple in this Quora answer - https://www.quora.com/What-are-the-best-book-rental-websites-in-India/answer/Pankaj-Chobharkar . Most of them seem to have converted to B2B model i.e. renting books to educational institutions and offices.
Librarywala and Doorstep books seems to be still targeting consumers and covering most cities in the country starting at 500-600/month. Would you be willing to spend such amount on renting single book every month?
Also check if there are book reading facebook group in your city, if there is one I would recommend sending this need gap to them for a comment.