If you can't find a boy of the appropriate age in any census records, the most likely reason is because the child died.

I've looked on the New Jersey State Archives death record index database, which goes up to the year 1900, and I didn't find anything for a young boy named David, either for the surname Pickholtz or Bernstein. But I'm not convinced that this index database is complete. Plus, if the death occurred in the early 1890s, there might not have ever been a death certificate filed with the county courthouse. I don't believe it was until 1900 or so that local or state governments began to consistently keep vital records. 

You could also try looking in the Philadelphia death records, to see if there is something relevant there.

There is a person I have used, who goes once a week to the NJ State Archives in Trenton. She can look directly at records and indexes there, many of which are not available online. Her site is at the following, and her rates are very reasonable: http://www.bringoutyerdead.com

Another option is to contact someone who is associated with preserving the Alliance colony. I recall reading that there is either small museum there, or someone who is in the process of starting a museum. They may have information about who was living at the colony in certain years, and may know of any deaths that occurred there.

Good luck finding what you are looking for.
--
Michele Lock

Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Rabinowitz in Papile, Lithuania and Riga, Latvia
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