This has been my brick wall for 8 years

My Great Great Grandfather was one Thomas Devaney, born in Ireland around 1856. My first sighting of him is in 1881 where he is single, and working in a pub.
In 1882 he married my Gt Gt Grandmother, Annie Morgan in Liverpool. Father's name on the marriage certificate is Patrick Devaney, deceased, Licensed Victualler.
Thomas and Annie had 4 children: Michael, John Patrick, Mary Gertrude and Joseph.
In the 1891 census Thomas is working in a pub in Cheshire, while Annie and the children are still at home in Liverpool.
Later on in 1891 Thomas died in Liverpool workhouse [TB]
I have no idea when Thomas came over from Ireland, or if his Father Patrick came too, nor who is Mother was.
Family hearsay has it they were from Mayo, but I have no concrete evidence of this, and actually despair of even ever finding a county for him.
Can only hope that some one has come across them in their own research and knows a bit more.
Many thanks for any help