Hi and welcome to the forum.
To assist anybody trying to help, here is the 1871 census
RG10; Piece: 3761; Folio: 17; Page: 28
159 Limekiln Lane, St Martin, Liverpool
James Biggins Head Widr 59 Stone Mason Ireland
Patrick Son Unm 32 Mason's Lab Ireland
Dennis Son Unm 29 Dock Lab Ireland
Honor Devine daur Wid 26 Ireland
Kate Devine granddaur 5 Lancashire Liverpool
Patrick Devine grandson 1 " "
and 1881 RG11; Piece: 3599; Folio: 44; Page: 82
159 Limekiln Lane, St Martin, LIverpool
James Biggins Head Widr 64 Stone Mason Ireland
Patrick Son U 40 Brick Layer's Labourer Ireland
Annie Devaney Daur W 36 Ireland
Catherine Granddaur 13 Bay Maker Liverpool
Patrick grandson 11 Scholar "
Can you tell us what your assumption of the date of arrival in Liverpool is based on? it would be fair to assume it was prior to 1866 - do you have knowledge that the marriage took place in England rather than Ireland?
Have you tried the
IGI and also the
LDS Pilot Scheme for the births, at least you have three approximate names and dates, rather than just one person, so if you come across them hopefully it will be with some certainty.
If you look on our Websites Board there are also some suggestions as to online sites available for Ireland.