Thanks again, Frances. But I'm afraid these don't seem to be my lot either:

The John James Quiggin in Sale, Cheshire in 1881, is at Westminster Terrace (Douglas), parish of Conchan in the 1891 census, a joiner, with his Manchester-born wife Mary Elizabeth and seven children, whereas my James McQuiggin is with his 2nd wife, Elizabeth also from Manchester, in Fancy St with his son James (1874) and two later daughters.

The one in Everton in 1881 is unmarried, whereas James McQuiggin had been married to Louisa since 1877 (according to Brian Lawson's index). This one is also a bread shop manager, which is perhaps a bit of a stretch for a boatman.

Maybe James McQuiggin (1850) and family were visiting relatives in Ireland at the time of the 1881 census!

Interesting as it would be to find them in 1881, my big hope is to find out more about James McQuiggin junior's death in 1905, and at least track down a death certificate.