I find no instance of anyone by the name of Hannah COONEY arriving at a US Port born 1881 +/- 2 years. But I do find a man named Dan or Daniel COONEY arriving at the Port of NY 20 times, as a member of the ship's crew.
Name: Dan Cooney
Arrival Date: 4 May 1920
Birth Date: abt 1878
Ethnicity/ Nationality: British (English)
Port of Departure: New York
Port of Arrival: New York, New York to Norfolk, Virginia
Ship Name: Turret Crown