Hi Susan
I think the best thing for you to do is to get a copy of the marriage certificate and see just who James's father is. It does seem a mystery.
With the information you gave me, I have been able to build up some history on Julia's parents. I have some manx informatio myself and the rest was supplied by Brian Lawson.

1841 census Ramsey 2 15 83
Cannell Isabella 60
Cannel Catherine 20
Cannel Christian 15

1851 Ramsey College Street
Cannell Isabella Head widow 70 born Maughold
Cannell Christian daughter unmarried 29 dressmaker born Ramsey
Cannell Lucy unmarried 26 born Ramsey
Carr Robert F Grandson 16 born England
Carr Julia Grandaughter 10 scholar born Ramsey
Carr Albert grandson 5 scholar born Ramsey

I'm not sure why Robert, Julia and Albert are listed as Carr they later become Martin.

Christian and Lucy are daughters of Thomas Cannel and Isabella Looney

Cannell Julia is daughter of Allen Martin and Christian Cannell born 1841 Ramsey (Morman index)

1851 Census Ramsey King Street
Martin Allan head married 33 Painter born Ramsey
Martin Ann wife 29 born Ramsey
Martin Robert son 8 Ramsey
Martin William son 2 born Ramsey
Martin Allan son 3 months born Ramsey

This is Allen Martin and Mary Ann Teare who married 1840 Maughold

1861, Ramsey, district 3, schedule 98, College street
Cannell Isabella head, widow, 83, not employed, Maughold
Cannell Christiana, daughter, unmarried, 36, dressmaker, Ramsey
Cannell Rhoda L, daughter, unmarried, 33, dressmaker, Ramsey
Martin Julia C grand daughter, unmarried, 19, dressmaker, Ramsey
Martin Albert grand son, 14, scholar, Ramsey

It would seem to me that Christian Cannell and Allen Martin never married due to the fact that he was already married.
He fits in with later information ie he is a painter

1861 Ramsey, district 2, schedule 125, King Street
Martin Edward head, widower, 87, no occupation, Ramsey
Martin Allen, son, married, 42, master painter, Ramsey
Martin Ann, daughter in law, married, 40, painter's wife, Ramsey
Martin Robert Teare, grand son, unmarried, 19, assistant painter, Ramsey
Martin Allen, grand son, unmarried, 12, scholar, Ramsey
Martin Henry, grand son, unmarried, 10, scholar, Ramsey
Martin John, grand son, 5, scholar, Ramsey
Martin William, grand son, 3, Ramsey
Martin Alice, grand daughter, 7, Ramsey

1881 8 King street Maughold
Allen MARTIN
Head M Male 62 Isle of Man, England Painter
Ann MARTIN
Wife M Female 60 Isle of Man, England
W. MARTIN
Son U Male 19 Isle of Man, England Sailor
C.A. MARTIN
Daughter U Female 17 Isle of Man, England
W. MARTIN
Son U Male 21 Isle of Man, England Sailor

I think Allen Martin died 1878 Maughold aged 78