Coleman Family

I want to trace my Irish roots but have little information.

My father, Albert Thomas Coleman, was born on 27 December 1905 at 161a Walton Lane Kirkdale Liverpool, to Michael Coleman, Engine fitter, journey man, and Agnes Coleman, formerly Curran: registeredon 12 February 1906 in West Derby 1906 register.

His father may have been Michael (Thomas maybe) Coleman born on 2 May 1870 in Cork, who died in Liverpool in 1909.
(Ireland Catholic Registers 1655 -1915).

Agnes Coleman nee Curran, was born, it seems, in 1879 in England and married Michael (maybe Thomas) Coleman in January 1990 in West Derby Lancashire.

Any help would be most welcome.