Hello Sue, we are going as fast as we can, so far it only mentions, Isle of Man for John Corkhill, no Parish mentioned yet.

14 Oct 1876 Waimate
Sophia Annie CORKHILL
Father: John Corkill age 39 Isle of Man
Married: 2 Oct 1864 Christchurch, N.Z.
Mother: Sarah Jane Corkhill formerly Powell age 29 Gloucestershire, England.
Informant: Sarah Jane Corkhill Mother of the Child, Waimate.

30 June 1881 Waimate
Francis Worthington CORKHILL
Father: John Corkhill Farm Contractor age 44 Isle of Man
Married: 1 Oct 1864 Christchurch, N.Z.
Mother: Sarah Jane Corkhill formerly Powell age 35 Gloucestershire, England.
Informant: Sarah Jane Corkhill Mother of the Child, Waimate.

And some confirmation of John Corkhill in Waimate, N.Z.

www.rootsweb.ancestry.com/~nzlscant/wrights.htm

Wright's Australian and American Commercial Directory and Gazetteer

Published in New York in 1881 and 1882-83 was an early effort at providing New Zealand with a national directory.

Waimate, Canterbury, 33 miles S.W. from Timaru It is on the creek of the same name. There are the usual official buildings, with three churches,
schools and other edifices. Agriculture is the industry of the district. The population of the county is almost 4000, of the township over 2000.

Trades and Professions
Builders, &c. - Corkhill John, Dancoh Samuel, Doig Stuart, Guildford Wm, Lane Frederick & Richard, McLean Alex., McMimimam John, Ottoway George, Pearson John