In one of your earlier messages you asked about the 1871 census. You might have got the details since then but if not -

1871 RG10/5776 f.169 p.22 sch.84
14 Fort St, Douglas, Onchan (district 7a)
James Cottier, head, m, 54, Sawyer, Douglas, Isle of Man
Isabella, wife, m, 49, wife of do., Edinburgh, Scotland
Margaret, d, unm, 24, dressmaker, Douglas, Isle of Man
William, s, unm, 17, stone mason, do., do.
Charles, s, unm, 14, trader, do., do.
Sarah, d, 11, scholar, do., do.
Walter, s, 7, do., do., do.

So as you suspected they must have married between 1871 and 1881. Don't know if that helps.