If your relatives died prior to 1949, their NYC death records are likely on FamilySearch.org. If you find the extracted record there, the image (front and back) of the actual death certificate will be available, for persons who know how to download the images. The folks at the Facebook Group 'New York City Genealogy' are able to get the images for those who request them, if a death record is found on FamilySearch.
On the images that I have, the funeral director's names are written, along with their address. If you can somehow locate those individuals, perhaps you can find out more about the congregation that your family members belonged to.
On the other hand - since funerals did not take place at synagogues, there might not be a reason to write such information down in any sort of record.
One other way to figure out what congregation your family belong to - on a marriage certificate, the name of the rabbi will be written. If your great grandparents had children who married in NYC, you might be able to get a rabbi's name that way, and then figure out the corresponding synagogue. The images of NYC marriage certificates I have show both the rabbi's name and address. A newspaper wedding announcement or an obituary might also help you out, though it is my understanding that these were not so common for NYC.
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus