You buy IOM certs (from 1878 for births and deaths, and from 1884 for marriages) through www.gov.im/registries/general/civilregistry/ - see "Contacts" at the top of their screen. There are a few earlier registrations shown on Brian's indexes.
For anything earlier than those dates (and also for some of the above records up to 1900) you can see the entries on LDS film ordered for a small fee through a local Family History Centre - and there are lots in NZ! See in phone book under "Church of Jesus Christ of Latter-Day Saints". They welcome non-members.

Yes, Brian's marriage index has COMISH, John, marr. 10 Jan 1884, C, arb, 1, KELLY, Emily. That fits with daughter Emily Annie COMISH being born on 24 May 1886.
And the IGI has John's father as JOHN, and Emily's father RICHARD KELLY, as you say.

The IGI also has:
name: Robert Corkill
event: Marriage
event date: 28 Dec 1868
event place: Braddan, Isle of Man
gender: Male
marital status: Single
father: Will Corkill
spouse: Martha Gelling
spouse's marital status: Single
spouse's father: Will Gelling
digital folder number: 004495611

Or have you already researched the Corkills?

Sue