Ancestry.com has a database titled New Jersey, Naturalization Records, 1878-`1945 that contains 960 people recorded as being born in Greece.
If you do not have a subscription to Ancestry.com, remember that you can access the program at most of your local libraries for FREE.
Description of database:
Naturalization is the act and procedure of becoming a citizen of a country, in this case, a citizen of the United States. The records involved in this process include declarations of intention, petitions for naturalization, certificates of arrival, and oaths of allegiance.
Although all of these forms appear in this collection, only the petitions for naturalizations were indexed. So, once you locate your ancestor’s record, make sure to check the surrounding images to see if more information is available.
The information that may appear on the petition forms includes the following: name, gender, age, birth date and place, petition date and place, date and place of arrival in the US, spouse name, and (if the applicant was a child) parents’ names.