Thanks Frances. I think this is a different family, however:

[from Browns 1881 directory]

McQuiggin, Felix, mariner, 1 1 Water-lane
McQuiggin, James, mariner, Postoffice-lane
McQuiggin, Patrick, fishmonger, 17 Postoffice-lane

(1871) 13 New Bond Street, Douglas RG10/5775 f4? p8 sch34 (cd9)
John McQuiggin H m 29 Car driver IOM [1842]
Mary “ w m 28 IOM
Mary “ d un 9mo. IOM

(1881) 8 Post Office Lane, Douglas (Dist 4a) RG11/5603 p.28 sch.160
Jno Jas McQuiggin h wid 35 Car driver Douglas [1846]
Mary d un 13 scholar “
Catherine d 6 “ “
Elizabeth Clackett boarder un 30 Domestic servant

OR

(1871) 10 Water Lane, Douglas RG10/5776 f93 p27 sch156 (ED4) (cd187)
Hugh McQuiggin H m 56 Tailor Ireland [1815]
Bridget “ w m 48 [2nd wife] “ [1823]
Jas “ s un 21 Boatman IOM [1850]

MC QUIGGIN, James, married 25 Jul 1877 D A2 67 CAUGHERTY, Louisa [Lawson]

MC QUIGGIN, Louisa, 28, buried Bra, 3 Jun 1881 [Lawson]

MC QUIGGIN, James married 13 Nov 1881 D A2 113 BLITHING, Elizabeth [Lawson]

(1891) 5 Fancy Street, Douglas RG12/4687 f.39 p. sch.17 (4 rooms)
James McQuiggin H m 41 Mariner Douglas (1850)
Elizabeth McQuiggin w m 43 [2nd wife] Manchester
James s 17 Douglas (1874)
Sarah J. d 8 Manchester (1883)
Martha d 5 Douglas

I have tried various spellings, on Ancestry, Familysearch and findmypast.