I am looking for birth records for the children of David Nechemias and Etta Ehrensaal. From census records, I have Beatrice (b. abt 1897), Helen (b. abt 1904), Sidney (b. about 1907) and Roselyn (b. abt 1911). The first three children should be indexed in the NYC birth index but I cannot find any of them. In particular, I have an estimate of Sidney's birth date from other records as 19 Jun 1906, but I could not find any plausible matches for him even without constraining his last name much.
From the city directory and census records, I am reasonably sure that the family actually did live in New York, at least starting in 1904, because the NYC directory shows a David Nechemias (drygds) at 133 Harrison Ave, and the 1910 census shows David Nechemias's occupation as "dry goods / own store." I have not found this family's 1900 census record.
I suppose the two obvious causes for my lack of success are a mis-spelled name or the possibility that they had children elsewhere. I've tried as many wild-card and spelling variants for the name as I could think of. I've tried doing searches unconstrained by geography. What am I missing? What should I do next?