In New York City they did issue death certificates for still born
deaths and they show in a separate part of the index >from the regular
deaths. You would have to ask the people who did the online index if
they incorporated the still born deaths or not into their work. The
Health Department is not going to be able to help because records of
that age have been transferred to the New York City Municipal
Archives.

I tried searching via Morse using the sounds like for the name and
filled in the age at death >from hours 0 to hours 23. I see a few
children who lived for minutes or hours but only saw three very early
(1880s) that had no age which I assume might be still born children.
So it is very possible the Italian Gen project did not incorporate the
still born index or that it is difficult to search them specifically on
their system.

My suggestion regardless would be to use the original index >from New
York City for 1918 and make sure you specifically look for the still
born deaths. Since you know more or less the exact date of death it
should not be too difficult to find but do not be surprised if the
certificate has mistakes with the name. (That is very possibly why you
are not finding it online even if they did include the still born
children in the online index.) It is also very possibly even though
the parents gave the child a first name that the death certificate
simply shows the child as "male" or "female" or possibly just "baby"
with the family name, i.e. Baby Gisser.

I would think this will work but otherwise a more laborious task would
be to try and look through the death certificates themselves. In New
York City they are sorted by borough and then by date. Since you know,
in this case, that the mother was at a hospital in the Bronx you could
look through the death certificates >from for that time period to see if
you find something that is not in the index.

The problem with the cemeteries is they do not keep that type of paper
work on file especially after nearly 100 years. And children's graves
were not as well documented and many times they put up smaller stones
(if any) and used softer materials which do not survive the years like
adult headstones. What you can look for at the cemetery is they
generally kept burial books in those years either in general or by
society which were kept by date, not name. Again since you know the
general date it should not be hard to find. Also some cemeteries are
good at keeping and sharing plot maps so you might be able to find a
child's grave on the map. It is also possibly however since the mother
died as well that they decided to bury the child with the mother. Some
times you see that on the headstone.

Allan Jordan