I know from Jean-Luc Chevillard that a Tamil text on meter, called the Yāpparuṅkalakkārikai, has a commentary (virutti) by one Kuṇacākarar that mentions a “book on Kannada meter.” He referred me to Ulrike Niklas’ edition and translation of the Yāpparuṅkalakkārikai and its commentary (Pondicherry 1993). Kuṇacākarar there discusses the similarities between the work he is commenting on, the Yāpparuṅkalakkārikai, and this Kannada text:

kuṇakāṅkiyam eṉṉum karunāṭakac cantam-e pōla makaṭūu-muṉṉilaittāy, avai-y-aṭakkam uṭaittāy.

containing addresses to a woman and [the author’s apologetic] submission to the assembly, as the treatise on kannaḍa prosody called guṇagāṅkiyam (tr. Niklas).

Niklas notes that the kārikai was composed in the later tenth century, and the commentary was probably composed around the same time: Kuṇacākarar is, in fact, said to have been the teacher of Amitacākarar, the author of the kārikai.

I was recently reading T. V. Venkatachala Sastry’s Kannaḍa Chandassu (Mysore, 8th ed. 2011) and he relates some interesting things about this Guṇagāṅkīyaṁ (as it was probably known in Kannada). Earlier, scholars had tended to identify this work with Nāgavarman’s Chandōmbudhi, which also contains addresses to a woman. The Tamil texts, however, are likely to be earlier than Nāgavarma’s Chandōmbudhi, which was composed at the very end of the tenth century. Śēṣagiri Śāstrī, however, was the first to note that Guṇagāṅka (or simply Guṇaga) are birudas, or titles, of the Eastern Cāḷukya king Vijayāditya III, who ruled from Vengi in the middle of the ninth century (843–887). The Cāḷukyas were enemies of the Gaṅgas, who would later patronize Nāgavarman. So here we have a reference to a work on Kannada meter that is now lost, but about which we know (a) that it was named for the Eastern Cāḷukya king Vijayāditya III; (b) that it was presented to the court (presumably of the same king); (c) that it spoke to a woman in the second person (conventionally the author’s wife); (d) that it was probably composed at more or less the same time as the earliest surviving work of Kannada literature, Śrīvijaya’s Kavirājamārgaṁ.

Here is the entry that I just made on PANDiT, the Prosopographical Database for Indic Texts.