When their children married, did they do so in a synagogue? If so there may be further records beyond the civil marriage certificate (I am not the person to ask for details, but there are people either here or on Jewish genealogy sites who can help).
Amsterdam marriages, but not births, are currently on Genlias.
The closest I can find are ones with the patronymic as "Levie" or similar.
e.g. Philip Levie van der Velde m. Grietje Nathan Drukker 1850 Amsterdam
(there are two other marriages around the same time that could be possibles but both those had children who married in Amsterdam in the 1870s - this couple did not).
http://www.dutchjewry.org/amsterdam_inhabitants/JOODS_list.asp - here there are listed at the same street (Rusland) / page (535)
Filip Levie Velden, v.d. (b. 1821-09-26 )
Grietje Nathan Drukker (b. 1829-08-22 )
Leentje Levie Velden, v.d. (b. 1852-04-11)
Naatje Philip Velden, v.d. (b. 1854-09-25 )
v.d. stands for "van der", and the middle name should be the father's name; Leentje = "Leah" and Naatje = "Ann"?
familysearch.org/ does have the "Netherlands, Civil Registration, 1792-1952" records but only as images (not name searchable, but there are some indexes). You might be able to find the births for the kids there.