Robert Liggett’s marriage to Mary King was registered in Newry 1866 Volume 1, page 1035. If you order a copy of that civil certificate it should give both their fathers and their townlands which should enable you to trace the family back. Tradition was to marry in the bride’s church so that may be the place to look for her baptism and that of her siblings.
Looking at the statutory indexes for the children, I can see some that match, and some that are out by a year or two, so you might need to order them up to see if they are correct. (You can get a photocopy for 4 euros from GRO Roscommon).
James Liggett b 1867. No match. Two of that name born 1866, one in Newtownards and the other in Lurgan. Neither seems likely. William John 1868.One 1868 in Newry Margaret Ann b 1870. None that year. Nearest was born 1872 Banbridge Andrew Martin b 1875. One match in Banbridge 1875 Joseph 1880. No match. One born Jan – Mar 1881 Banbridge (spelled Leggate) Richard b 1882. Match in Banbridge Jul – Sept 1882. Spelled Liggate.
The townlands should be on the birth certificates to confirm they are the correct family. However this looks to be Robert and some of the family in 1901:
Griffiths Valuation shows that in 1864 there was a James Leggitt on plot 7 in Knocknanarny townland. That was a farmhouse, outbuildings and 26 acres. In 1867 it passed from James to William Leggitt. Then through the 1880s there were a number of changes which led to Robert & Moses sharing plots 7& 8 for a while. By 1900 Martine (ie Andrew Martin) had acquired both farms. They were still tenanted at that time but Martin bought them under the Land Act in 1909 (ie with a government mortgage). Both were still in his name in 1929.
You can see that using the PRONI revaluation records:
Andrew Martin appears as just Martin in some of the records so I suspect that was the name he went by on a daily basis.
The farms on plots 7 & 8 are separated by a small bit of land (plot 11) owned by someone else. They are both on the modern Carrickrovaddy Rd, a few miles north of Newry. Easy enough to find today if should wish to do so.