Hi,
whre you able to find their marriae record in NYC?
I checked the database on the Italiangen.org website and found a possible record:

Barbella Giuseppina Aug 14 1904 Kings 6189
groom:

Amaro Ginno B Aug 14 1904 Kings 6189

I know names are off but maybe this record worth to be investigated better...
Most likely they were married in Brooklyn not in Italy being the bride born in the U.S.

Laura