You can find a research guide for New York passenger records here...
Finding New York Passenger Arrival Records 1820-1957http://home.att.net/~germanroots/ellisisland/nypassengers.ht...
Since New York passenger lists have only been indexed until 1948, you will need to know the exact date of arrival. See if you can find your parents citizenship papers, which should have this information.
Good luck with your search.