I wonder if it is this family?
1851
Piece: 2036
Folio: 475
Page Number: 22
Rocks Hill, Kingswinford
Joseph Cox 34
Jane Cox 38
Noah Cox 14
Mary Ann Cox 13
Elisabeth Cox 12
William Cox 11
Ann Maria Cox 10
John Cox 8
Charles Cox 6
Francis Cox 4
Sarah Jane Cox 2
Fanny Cox 3 Mo
1861
Household schedule number: 216
Piece: 2072
Folio: 61
Page Number: 45
Virgins End on South Street, Kingswinford
John Cox 44
Jane Cox 48
Elizabeth Cox 23
William Cox 22
John Cox 18
Charles Cox 17
Francis Cox 14
Sarah Jane Cox 12
Fanny Cox 10
Josiah Cox 8
James Henry Cox 7
Job Cox 5
Maria Cox 2
The kids are mostly easy to find with mother's maiden name of Morris
COX, MARY ANN MORRIS
GRO Reference: 1837 D Quarter in STOURBRIDGE UNION Volume 18 Page 335
COX, WILLIAM MORRIS
GRO Reference: 1840 M Quarter in STOURBRIDGE UNION Volume 18 Page 472
COX, ANN MARIA MORRIS
GRO Reference: 1841 J Quarter in STOURBRIDGE UNION Volume 18 Page 462
COX, JOHN MORRIS
GRO Reference: 1842 S Quarter in STOURBRIDGE UNION Volume 18 Page 425
COX, JOSIAH MORRIS
GRO Reference: 1843 D Quarter in STOURBRIDGE UNION Volume 18 Page 467
COX, FRANCIS MORRIS
GRO Reference: 1845 J Quarter in STOURBRIDGE UNION Volume 18 Page 447
COX, SARAH JANE MORRIS
GRO Reference: 1849 J Quarter in STOURBRIDGE UNION Volume 18 Page 516
COX, FANNY MORRIS
GRO Reference: 1850 D Quarter in STOURBRIDGE UNION Volume 18 Page 490
COX, JOSIAH MORRIS
GRO Reference: 1852 S Quarter in STOURBRIDGE Volume 06C Page 162
COX, JAMES HENRY MORRIS
GRO Reference: 1854 M Quarter in STOURBRIDGE Volume 06C Page 210
COX, JOB MORRIS
GRO Reference: 1855 D Quarter in STOURBRIDGE Volume 06C Page 190
COX, MIRA MORRIS
GRO Reference: 1858 S Quarter in STOURBRIDGE Volume 06C Page 219
Only "Charles" is not there

but there is a baptism
Name: Charles Cox
Gender: Male
Baptism Date: 17 Mar 1844
Baptism Place: Kingswinford and St Marys Chapelry ,Stafford ,England
Father: John Cox
Mother: Jane
FHL Film Number: 435779, 435780, 435781
and that fits with ones for Noah and Francis, for example
Noah Cox 11 Dec 1836 Kingswinford and St Marys Chapelry ,Stafford ,England John, Jane
Francis Cox 4 May 1845 Kingswinford and St Marys Chapelry ,Stafford ,England John, Jane
Possible marriage for the parents
Name: John Cox
Gender: Male
Marriage Date: 3 Apr 1836
Marriage Place: Saint Thomas,Dudley,Worcester,England
Spouse: Jane Morris
Francis pitches up in Illinois
Name:
Francis Cox
Event Type:
Marriage
Event Date:
12 Aug 1885
Event Place:
Grundy, Illinois, United States
Event Place (Original):
Morris, Grundy, Illinois
Gender:
Male
Age:
38
Marital Status:
Unknown
Race:
white
Birth Year (Estimated):
1847
Birthplace:
England
Father's Name:
John Cox
Mother's Name:
Sarah J. Morris
Spouse's Name:
Maggie Kneudtson
Spouse's Gender:
Female
Spouse's Age:
26
Spouse's Marital Status:
Single
Spouse's Race:
white
Spouse's Birth Year (Estimated):
1859
Spouse's Birthplace:
Norway
Spouse's Father's Name:
K. Kendtson
Note:
Pr Name: third marriage;
Did they all emigrate together or individually?