After years of research, I have concluded that Michael was a Nephew of James and Mary Malarkey (See Posting of 2005 & 2006) rather than a Son.
The Malarkey name came from an interpretation of the Mullarkey / Mularky Surname in Ireland predominately found in Galway, Sligo, and/or Mayo Counties.
Michael (Ire 1855 - > 1910) did marry Elizabeth O'Neill in Philadelphia (1881). Elizabeth (PA 1858 - 1890-1) was the oldest Dau of James O'Neill & Mary Unk O'Neill of Ireland.
Michael & Elizabeth had 5 children:
Lucy Malarkey Sherry (1882 - 1967)
John J. Malarkey (1883 - 1935)
Mary Malarkey McKenna (1886 - 1969)
James E. Malarkey (1887 - > 1950)
Elizabeth Malarkey (1890 - unk).
Still looking for any Descendants