Hi,
I think that Joseph and Mary, married in 1887 would have been your GGrandparents and going back a generation earlier I can find the Marriage of a Moore Laverty to a Catherine Jane Mullan in Derrykeighan Church of Ireland, Ballymoney on 4 Sept 1860. The fathers' names were John Laverty and William Mullan. Children of the couple were :-
15 June 1864 Margaret registered in Dervock
14 May 1866 Elizabeth
9 May 1870 Moore registered in Dervock
11 may 1872 Isabella registered in Dervock
24 Oct 1874 William john registered in Ballydivity
30 jan 1877 Catherine Jane.
Mary was possibly born before 1864 when Civil Registration of births started.
Regards