Just found more information. John Joseph Cunnigham, born 1864, was son of James Cunningham and Bridget Langan, who lived in Cashel, Killala, County Mayo, Ireland. James and Bridget also had the following children: Mary (1863), Peter (1866), Catherine (1868), Martin (1871). Martin also moved to Scranton PA.
I am still tracing back further, but I suspect that James was son of John Cunningham, born about 1770 and had brothers: Peter, John Jr and Thomas. There were probably a number of sisters, but I haven't been able to sort that out.
There is a chance that John Cunningham Sr was part of the exodus from Ulster, after the Battle of the Diamond in 1796, but I am still tracing that.