Eddie,
I will give the first lot of information now and follow it up with more later.
27 Apr 1850 Robert Parker married Anne Graham in Ballymena Registrars office. A parent search on the IGI gives one child for this couple, Robert, Christened in Connor Presbyterian Church on 27 Apr 1850. From Ancestry Ireland I was able to find that Robert Parker's (Sen) father was Simon.
I found two other Parker marriages where the father was Simon:-
14 Dec 1847 Robert Hill to Elizabeth Parker in Connor Presbyterian Church
15 Mar 1849 William Parker to Mary Ann Montgomery Connor Presbyterian Church.
Regards