You didn't say how much you knew about the children. Do you know when and where Eliza or John married?
Here are a few things probably for their son John.
Pvt John Williams
Birth 29 Dec 1841
Pennsylvania, USA
Death 21 Dec 1909 (aged 67)
Philadelphia County, Pennsylvania, USA
Burial Westminster Cemetery
Bala Cynwyd, Montgomery County, Pennsylvania, USA
Plot Section: Evergreen, Lot : 327
Memorial ID 58087274
Son of William and Jemima (Russell) Williams.
WILLIAMS – On December 21, 1909 JOHN WILLIAMS son of the late William and Jemina Williams age 68 years. Relative and friends of the family, also survivors of the 73d Regiment P.V. and Union Veteran Legion are invited to attend funeral on Friday at 2 o'clock from his late residence, 172 Carson St. Manayunk. Interment at Westminster Cemetery. (Philadelphia Inquirer, 1909-12-21)
https://www.findagrave.com/memorial/58087274/john-williams------------
John Williams
born 29 December 1841, Pennsylvania
died 21 December 1909, Philadelphia
died at 172 Carson, Ward 21, Philadelphia
white, male, married
father: Wm Williams, born in Pennsylvania
mother: Jamima Russell, born in Pennsylvania
informant: J T Ryan, Manayunk [the undertaker]
buried: Westminster Cemetery, December 24, 1909
[Manayunk is a neighborhood in Philadelphia]
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I found this for Jemima Russell. It might be the one you are looking for:
Bucks County Tax Records, 1814
"Poor children between the age of 12 and 5 years"
parents names: Thomas Russell
chlidren's names: Polly Russell, Kesiah Russell, Jamimah Russell, Malinda Russell
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There is a William Williams baptized at Hilltown Baptist Church, Hilltown, Bucks County, on December 8, 1799. He was dismissed from the congregation January 16, 1819
4 other Williams baptisms on the page. on September 29, 1799: Isaac, Benjamin, Eleanor, and Thomas Williams
There is no guarantee that is the man you are looking for. It is a common name.
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And I'm assuming the man you are looking for is white. There is a black William Williams on the records in Bucks County about the same time.