According to US census records (Oregon and Washington), my g. grandfather John Thomas Mullarkey was born in Ireland around 1840.He married Julia Ann O'Hara. Their 1st and 2nd son's, Thomas John and Burnett, were born somewhere in Pennsylvania approx. 1864 and 1867 respectively. I have located Catholic church records which document the birth and baptism's of their 3rd son James b. 1/24/1869, 4th son Edward Francis b. 9/4/1871 and 1st born daughter, my grandmother, Mary Ann b. 7/1/73 all in Coos Bay, Oregon.The 1880 Oregon census includes John Thomas's father "John" age 80 living with the family in Coos Bay. After 1880 the family moved to Seattle, Washington.
From the similarity in given names, ages andbeginnings in Pennslyvania it appearslikely you and I are looking at the same core family.I have been told that Irish families of that time generally followed a strict set of rules when naming their children. You mention Mary born approx. 1835 in Ireland who named her son John.She could possibably be my g. grandfather John's sister.
I have been unable to locate immigration or marriage records for my g. grandparents orfind them in Pensylvania's census records. My g. grandfather at least after moving west always listed his occupation as "miner"
Would appreciate communicating by e-mail (firstname.lastname@example.org) to compare more information.