Alan,

Manifests from that time frame may give you nothing more than his name and the country from which he came.  It varied by shipping line at that time.

Have you searched using soundex?  ZUCKER may be listed as ZUCHER, or something else.

The first name could be listed as various spellings of Hirsch, or Zvi.

The name could also have been transcribed incorrectly into the index.

He also may have entered through a port other than NY, including coming down through Canada.  I was surprised to see some of my family entering through Canada and then down to NY.

Regards,

Sherri Bobish