Today I went to the library and look up Bonner's Extreme Poetry regarding the date of Kaviraja.
In his Appendix I (p.269), he wrote: "Raghavapandaviya of Kaviraja (c. 1175, Kadamba court)."
In the main text (p.232), he wrote: "... Kaviraja's Raghavapandaviya, a work written under the patronage of the Kadamba monarch Kamadeva (r.1181-1197), but read and admired well beyond its immediate Deccani locale." On p.140, he wrote to the same effect.
In the notes to p.140, he wrote: "For information on Kaviraja's background, see Pathak 1905; Krishnamachariar 1937: 187-188; and K.A. Nilakanta Sastri 1976. In the bibliography he gave the following entries:
> Krishnamacharier, M 1937 History of Classical Sanskrit Literature. Delhi: Motilal Banasidass, Reprint 1989
> Pathak, K.B., 1905 "On the Age of the Sanskrit Poet Kaviraja" Journal of the Bombay Branch of the Royal Asiatic Society 22:11-16.
> Sastri, K.A. Nilakanta 1976 A History of South India: From Prehistoric Times to the Fall of Vijayanagara. 4th ed. Delhi: Oxford University Press.
I have found on Google Books a book by V.V.Mirashi 1975 which cites various dates for Kaviraja:
K.B. Pathak 1182-1197
Based on these information, tentatively I am dating Kaviraja to 1182 A.D. (Updating the corresponding date on South Asian Canonical Text Page)