FamilySearch.org has a new FREE database titled Rhode Island, District Court Naturalization Indexes, 1906-1991 which has 1,201 index cards for people born in Greece.
The Index card contains the following information:
Given name or names
Title and location of court
Country of birth or allegiance
When born (or age)
Date and port of arrival in U.S.
Date of naturalization
Names and addresses of witnesses
You might also be interested in a previous post - United States, New England Petitions for Naturalization Index, 1791-1906 which has 2,075 index cards for people born in Greece.