National Archives: Famine Irish Collection
The Famine Irish Collection at the National Archives comprises two searchable resources: "Famine Irish Passenger Record Data File" and "List of Ships that Arrived at the Port of New York During the Irish Famine." Both cover the years 1846 to 1851, inclusive. The first has 604,596 records of passengers arriving in New York—70% of whom came from Ireland. The second offers a bit more information on the ships that brought them over—including the total number of passengers on each voyage. Together they should satisfy your Irish-famine-migration-to-New-York needs.