There are 31 Zylbernadel marriages in Poland, on record (and one divorce). 19 of them were in Belzyce and 5 were in Kazimierz Dolny (Krakow). Of the rest, there was one each in in Lublin, Markusow, Chodel, Kurow, Konskowola, Ozorow and Pulawy. The divorce was in Lublin, in 1837.
Only 15 of the marriages were males, who's children would carry the name onwards. One of those, Benjamin in 1829/1830 and 1831, re-married.
The only Izrael on record to marry was in 1840, in Kazimierz, but that would have been far too early for him to have been Jacob Silverneedle's father. Jacob was born 34 years, later. The identity of Jacob's father, whom he gave as Israel, remains a mystery.
N.B. Names that are probably male are shown in blue
Belzyce:
1829(or 1830) Benjamin married Szandla Ayzenberg
1831 Benjamin married Mindla Furtag
1832 Cyrla married Joel Korn
1842 Haia married Moszek Rayss
1842 Laja married Szmul Morgenstern
1842 Sura married Josef Ulman
1844 Szmul married Ryfki Rayzli Cang
1848 Golda married Wigdur Fensler
1849 Rysia married Moszek Josef Moryl
1851 Berek married Czarna Sztarg
1851 Necha married Jonas Cymerman
1858 Cywia married Lejba Moszek Liberman
1861 Manas Matys married Ryfki Mirla Tyszblat
1865 Abram Uszer married Maryanka Morgenstern
1882 Nojech Zilbernadel married Bajla Denenmark
1885 Szmul Moszek Zilbernadel married Ruchla Cajg
1891 Czarna Malka Zilbernadel married Szmul Icek Cwajg
1895 Ita Zilbernadel married Lejba Gerszek Bilet
1901 Sura Perla Zilbernadel married Abram Lejzor Lioberbaum
Kazimierz:
1833 Icek Szmul Abramowicz married Perla Laia Ledersznayder
1840 Izrael married Chaia Hecht
1864 Dyna married Symcha Kohen
1864 Abram married Czarna Uman
1900 Blima married Cala Kugel
Lublin:
1837 Perla Zylbernudel divorced Leyb Rozenber - Lublin
1898 Chaim Josif married Laia Tuler - Lublin
Other locations:
1839 Mindla Zylbernadel (nee Fingiertman; father Icek; mother Bayla) married Majer Weber (father Szmul; mother Hana) - Markuszow
1870 Abram Icek married Szandla Berkowicz - Chodel
1877 Berek Zylbernudel married Chaia Szpilberg - Kurow
1879 Josek married Sura Finkelsztejn - Konskowola
1887 Berek Zilbernadel (mother Golda; father's name missing!) married Slawa Diiament - Ozarow
1895 Abram Zylbernudel married Chindla Szlufman - Pulawy