Do you have any approximate or exact dates, or villages? Did the family come from Samoa or American Samoa? Ancestry has the 1920 American Samoa census online. (It also has the 1910, but that is useless for Samoans, fine for Naval personnel).
If you have a village, try doing a search on it on Google. This may pick up entries from there on Familysearch. I'm not sure whether that will work,but it's worth trying.
When did the family come to America? What names are on their papers?