I wrote an overview over Vijayanagara and religion a while back, including a part on sources. Not sure about modern, but I found them interesting and fun (esp. the Wagoner one), it's a mix of a book and two articles:

From that anwer:

"For a good overview on Vijayanagara see Rao, Nalini, Royal Imagery and Networks of Power at Vijayanagara – a Study of Kingship in South India, Delhi 2010.

More focused on the political situation and religious identity there: Sinopoli, C. M.: ''From the Lion Throne'', JESHO Vol. 43, 2000, p. 364-398. (if you have jstor access)

A detailed look at court ceremonies, clothing and art is Wagoner, Philip B.: ''´Sultan Among Hindu Kings´: Dress, Titles and the Islamicization of Hindu culture at Vijayanagara'', in: The Journal of Asian Studies 55/4, 1996, p. 851-880. (again on jstor)"

Hope this helps!