I searched the federal 1930's census for NY state, Onondaga
county, Syracuse. I don't remember the emuneration district for where the hospital was located. but I do remember a name that you can search on to bring you to the hospital records for 1930, Vera Procopio. Once you are in the records for her, you can see the other poeple at the hospital and try to narrow possibilities by age, my mother- in -law was born in June 1929, so at this time of census( look on the top of the paper to read the date, perhaps it says Feb 1930? so for my relative, she would be 8-9 months) Then look thru the list at ages for children around that age. It may give you some idea. I can't get in now as I don't have a subsciption to exactly check. Hope this helps. good luck!