I have 2 and they're both Irish.
Michael Shaughnessy my 3 x GGF, (theoretically should be easier to find than the other one) his son Patrick my 2 x GGF born 1846 was from Galway, Ireland, that information is on the 1911 England Census.
I have a baptism record for Patrick that makes sense.
I have Michael's name on Patrick's, 23 Jan 1867, Newcastle Under Lyme, Staffordshire, England marriage record. Michael is described as labourer, sometimes marriage records from that time in addition to giving the father's name say deceased, it wasn't a requirement so if it doesn't say deceased the father could be dead or alive.
There are 7 baptism records that may be correct for Michael Shaughnessy in Galway between 1794 and 1817, it has not been possible to connect any of these records to this Michael Shaughnessy. His oldest child was born 1834.
The family or perhaps just Patrick would probably have arrived at Liverpool after leaving Ireland. There several records for deaths of people named Michael Shaughnessy in the Liverpool area including the workhouse between 1847 and 1860. He could have died in Ireland, there are records for the death of many Michael Shaughnessys in Ireland during this time period. I can't make any of them connect to Patrick's father, there just isn't enough information.
There are several 1851,1861,1871 census records for Michael Shaughnessys in the Liverpool area, and in Staffordshire. If he went to England he may have remarried in England as none of these records have a wife named Mary as shown on the baptism record.
I have records for Patrick including his 1846 baptism, England censuses from 1861-1911, marriage, death, burial, all his kids names and other records, but nothing that helps find Michael.
Edit: clarification