I think this lot all, somehow, manages to hang together, even though some of the birth-years are far from consistent:-
07 Jul 1842 Barty QUIGLEY m Honor HUNT Kilshalvey, Co Sligo
1851 Bartholomew (b 1808) & Hannah (b 1816) COGLEY (Quigley?) Austin Houses, Wigan
James (1843), John (1845) all b Ireland
1861 Bartholomew (b 1806) & Hannah (b1824) QUIGLEY 14 Boyswell Lane, Wigan
James (1843), John (1845) all b Ireland
Bartholomew (1852), Thomas (1856), Catherine (1848), Michael (1860) all b Wigan
Q4 1860 Michael QUIGLEY mmn HUNT b Wiga
Q2 1864 Mary QUIGLEY mmn HUNT b Wigan
1871 Bartholomew (1816) & Ann (1829) QUIGLEY Boys Well Lane, Wigan
James (1845) all b Ireland
Thomas (1855), Mary (1864) b Wigan
1881 Bartholomew (1815) & Ann (1831) QUIGLEY 10 Shaws Yard, Wigan
James (1846) all b Ireland
Thomas (1856), Mary (1865) b Wigan
Q1 1887 Bartholomew QUIGLEY (b 1817) died Wigan
Q4 1890 Ann QUIGLEY (b 1831) died Wigan
I’m sure the 1851 census entry must be QUIGLEY but, for some strange reason, I can only access the transcription; it offers me the original but, when I ask for it, it gives me a totally different page.
We're told by Wexflyer that the Irish name FEIGHNEY is often anglicised to HUNT, so the 1842 marriage could well be between Bartholomew QUIGLEY and Honor/Hannah/Ann FEIGHNEY. If so, I might have found her baptism:-
14 Jun 1819 Anna FEIGHNY to Patrick & Maria (nee HALY) Ahamlish, Sligo
Sponsors: James HALY and Honoria FEIGHNEY
James QUIGLEY (brother of Mary) consistently gives his birth year as 1843, place Sligo, which fits nicely with the 1842 marriage cited above.