John Quigley & Catherine McClannan

[Murphy]

I am trying to get more information on my paternal gg.grandparents above. Specifically when and where in Ireland they were born.
I've tried searching in Dublin Archives - but, based on the info I have below, the staff there suggested trying to find the marriage records in England.
That's where I'm struggling, as I haven't been able to find one so far.

Name -
John Quigley & Catherine MacClannan

Date and place of birth - both Ireland, places unknown - John c.1815 Catherine c.1826

Names of parents - unknown

Date and place of baptism - unknown

Details of each of his or her marriages -

1 John Quigley & Margaret Quigley are shown in the 1841 Census living at Back Chester Street, Birkenhead. Both born Ireland.
Children listed - Patrick Headin 13, Bridget Headin 8, Catherine Headin 6, Michael Headin 4 & Mary Ann Quigley 1.
The three eldest born in Ireland - Michael & Mary Ann born Birkenhead.
Margaret's previously married name was Headin (Heden) - the 4 named children being hers by another marriage, plus her child Mary Ann with John Quigley.
Her maiden name is shown on Mary Ann's BCert. 18 Oct 1939.

2 John Quigley & Catherine Quigley (McClannan) - both born Ireland.
In 1851 Census living at 5, No.8 Court, New Bird Street, Liverpool
Children - Mary Ann 11, Margaret 2, Arthur 1 - all born Birkenhead

Occupation(s) - Shoemaker / Cordwainer

Addresses where they lived - and please list which censuses you have or haven't found him/her on.

1839 Back Chester St., Birkenhead - BC of Mary Ann Quigley 18 Oct 1839
1841 Census - Back Chester St., Birkenhead (as above)
1851 Census - 5, No.8 Court, New Bird St., Liverpool (as above)
1844 - 13 Jan 1844 Back Chester St., Birkenhead - DC of first wife Margaret Quigley Qtr. Mar Vol 19 Page 240
1849 - 4 May 1849 Back Chester St., Birkenhead - BC of son Arthur Quigley Qtr. Apr Vol 19 Page 397

I haven't found them in 1861,1871 or 1881 Censuses

Date, place and cause of death -

13 Jan1844 Margaret Quigley (Headin) - Back Chester St., Birkenhead. Cause - Childbed (assuming in childbirth) aged 39
25 Dec 1873 John Quigley aged 58 - 352 Price Street, Birkenhead - phthisis DC Qtr Dec Vol 8a Page 292

Date and place of burial / cremation.

Margaret Quigley (Headin) - unknown
Catherine Quigley (McClannan) - unknown
John Quigley - 29 Dec 1873 Birkenhead Flaybrick Cemetery - public grave

Details of will / administration of their estate - unknown

Memorial inscription - none