Maybe all these are Elizabeths children...
JONES, HUGH GOODWIN
GRO Reference: 1870 J Quarter in LIVERPOOL Volume 08B Page 7
JONES, JOHN GOODWIN
GRO Reference: 1871 D Quarter in LIVERPOOL Volume 08B Page 140
JONES, STEPHEN GOODWIN
GRO Reference: 1867 M Quarter in LIVERPOOL Volume 08B Page 110
JONES, ROBERT GOODWIN
GRO Reference: 1873 S Quarter in LIVERPOOL Volume 08B Page 157
JONES, JOHN THOMAS GOODWIN
GRO Reference: 1874 S Quarter in LIVERPOOL Volume 08B Page 81
JONES, WILLIAM HENRY GOODWIN
GRO Reference: 1876 M Quarter in LIVERPOOL Volume 08B Page 160
JONES, ELIZABETH GOODWIN
GRO Reference: 1878 S Quarter in LIVERPOOL Volume 08B Page 149
All these do not help finding her marriage and Stephen 1867 is a problem. The only marriage around this period is the one that maddys52 found to Thomas in Birmingham 1869, this would make Stephen illegitimate but Thomas could still be the father.
ADDED. Maybe baptism for Stephen...
Stephen Jones. baptised 5 Feb 1867, All Saints, Liverpool. father Stephen, mother Elizabeth.
Looks like Stephen is one of these deaths...
JONES, STEPHEN 0
GRO Reference: 1867 M Quarter in LIVERPOOL Volume 08B Page 244
JONES, STEPHEN 1
GRO Reference: 1868 S Quarter in LIVERPOOL Volume 08B Page 26