With Jon C. Marten (q.v.), Cornelius Conyn was a founding member of the Conyn Dance Group. Based in Sydney, this small recital group were to spend a decade touring, with highlights being an appearance at a Royal Command Performance and 'an extensive Far East Tour in 1955, for the Arts Council in Indonesia'. The group also gave lectures for various educational forums such as the Arts Council.
Drawing on the experience of the dance company's Indonesian tour, Conyn and Marten co-wrote a novel, The Bali Ballet Murder (1961). It was the first in a 'trilogy of travelogue-detective stories'. Marten and Conyn intended to produce two subsequent novels, 'Murder in Tahiti' (source indicates the first and only edition of this work was published in Brussels; untraced) and 'Murder in Malaga' (unfinished).
Although Conyn has written a book about animal behaviour, A Zoo of My Own (1957), the main concern of his writing was dance. He published an illustrated booklet, Doris Niles : Interpreter of the Spanish Dance (1937), an illustrated history, Three Centuries of Ballet [1948], and during 1946-1947 was the 'major dance writer' for the arts-related journal, Australia.