Hi Roger,
I have searched the marriage records for Liverpool, and there is no record of them. So, yes, they were married in Galway and moved to Liverpool between the 1851 - 1861 census. I have them on the census returns in Liverpool from 1861 onwards.
It states on the 1891 census (see attached) that Mary and Patrick were from Galway. They had a son Michael who I'm assuming was born in Galway in 1858 before they moved to Liverpool.
If you have any volunteers who could look into this for me I would be more than happy to make a donation to the organisation.
I can also grant them access to my tree on Ancestry, where they will find other records that may help.
Thanks for your time and interest, best regards, Kenny.