1900 and 1910 census shows there were 2 surviving children of Patrick and Bridget.
Transcription records of Mount Olivet Cemetery in Reed City says Bridget's maiden name was Sullivan born 03 Feb 1838 died 04 Feb 1919 daughter of A Sullivan (findagrave.org).
In 1937 Martin James MONAHAN filed for his social security number while residing in Wynne, Cross county Arkansas stating he was born in Hoboken, Hudson Co NJ 10 June 1866 to Patrick Monahan and Bridget Sullivan (ancestry.com).
I find him listed in 1920-1940 census in Cross county AR wife was Minnie Lee Unknown born in Georgia in 1870 died 1958 and married about 1904 in unknown location.
Martin was conductor for the Missouri Pacific RR and died in their hospital in St Louis MO 26 July 1941. His wife did not know who his parents were (s1.sos.mo.gov).
Martin and Minnie are buried at Coghill Cem in Wynne AR (findagrave.com).