I'm an avid Cain(e) searcher. I got started in all of this in helping a friend who had the family story of a connection to Hall Caine. That launched my wonderful new hobby. Since that time I've had contact with many Cain(e) descendants with the same family story. So far I've only found 1-2 with actual connections--at least that I can prove.
I believe your Christiana Kinley md Thomas Caine ch 25 Nov 1804 German parish son of
John Caine & Isabel Teare who md 12 Feb 1793 Ballaugh parish.
William ch 24 Sep 1801 Jurby parish later md Jane Harvey Holmes
Philip ch 13 Nov 1808 Ballaugh parish

I'm not sure which Cain(e) line John belongs to. I believe he and Philip were buried in Braddan
Braddan MI Old Yard South #179:
In memory of John Cain who died in Douglas Aug 24th 1849 aged 73 years.
Also Philip Cain son of the above who died in Douglas June 25th 1858 aged
49 years. Blessed are those servants whom the Lord when he cometh shall
find watching Luke XII Chap XXX Verse VII.

If correct, that would make him born abt 1776. Of course, there are a bunch of Johns born at that time.
Again, if correct there are 2 John Caine wills--one 1849 German and one 1850 Braddan that might be for this John.
I don't have access anymore to researching the wills but would suggest that might be something for you to pursue.

1851 Marown
, 03-67, 088, CAIN, Thomas, Cottage Garth, Head, Married, 47, Ag Lab,
German
, 03-67, 088, CAIN, Christiana, Cottage Garth, Wife, Married, 45,Douglas
, 03-67, 088, CAIN, John, Cottage Garth, Son, , 10, , Marown
, 03-67, 088, CAIN, Ann, Cottage Garth, Daughter, , 8, , Marown
, 03-68, 088, CAIN, Jane, Cottage Garth, Daughter, , 6,
, 03-68, 088, STEELES, Richard, Cottage Garth, Stepson, Unmarried, 22,
Lead Miners Lab, England

Might find some leads via descendants of William
1851 Braddan
Union Mills
William 47 Jurby, Jane 37 Ireland

1881 Douglas
District Number HH Number Last Name First Name Place Relation Condition Age Occupation Born Census for
2 175 CAIN William 2, Shaws Brow H M 79 Formerly Clothier Jurby Douglas
2 175 CAIN Jane """" W M 69 Stay Maker Ireland Douglas