I am not sure if these entries are your family
From familysearch.com
Is ths Thomas the same as the next entry
Name: Thomas Rowan Linton
Event Type: Marriage
Event Date: Jan - Mar 1887
Event Place: Ballymena, Ireland
Registration Quarter and Year: Jan - Mar 1887
Registration District: Ballymena
Volume Number: 1
Page Number: 127
GS Film number: 101255
Digital Folder Number: 004179726
Image Number: 00314
Thomas
Ireland Births and Baptisms, 1620-1881
birth: 1 October 1868 Ballymena, Ant, Ire
christening: 102, BALLYMENA, ANT, IRE
residence: 1868 , , Antrim, Ireland
father: Robert Linten
mother: Ann Mc Ilhagga
so either Eliza or not
Samuel Linton
Ireland Births and Baptisms, 1620-1881
birth: 2 June 1864 0523,CLOUGH,DOWN,IRELAND
father: James Linton
mother: Eliza Magill
James Linton
Ireland Births and Baptisms, 1620-1881
birth: 25 June 1866 0831,RATHFRYLAND,DOWN,IRELAND
father: James Linton
mother: Eliza Magill
Eliza Jane
Ireland Births and Baptisms, 1620-1881
birth: 21 November 1868 Ballymena, Ant, Ire
christening: 104, BALLYMENA, ANT, IRE
residence: 1868 , , Antrim, Ireland
father: James Linton
mother: Eliza Magill
Joseph
Ireland Births and Baptisms, 1620-1881
birth: 9 December 1870 Ballymena, Ant, Ire
christening: 117, BALLYMENA, ANT, IRE
residence: 1870 , , Antrim, Ireland
father: James Lenton
mother: Eliza Magill
Robert Linton
Ireland Births and Baptisms, 1620-1881
birth: 3 June 1874 Ballymena, Ant, Ire
christening: BALLYMENA, ANT, IRE
residence: 1874 , , Antrim, Ireland
father: James Linton
mother: Eliza Magill