Statutory birth registration started in Ireland in 1864. I searched the records 1864 -1878 but did not see any births to James Given & Margaret. So it looks as though the 3 children you have found – who must all have been born before 1864 – may be their only offspring. I think I can see James in the 1901 census in Shanmullagh, and that he was Presbyterian.
When he was married in 1856 he was in Largybeg which is in the parish of Ardstraw. So if you know which Presbyterian church he attended in Ardstraw, then you could search its records for the children’s baptisms. There are several Presbyterian churches in that area. This link explains what records exist, parish by parish:
Normally you can inspect them in PRONI but it is closed indefinitely at present due to coronavirus.
Can’t help you with William Given. If he died before 1864 there’s probably no record of that. I searched the records 1864 to 1901 but did not see a death that fits with that age. I did notice this William who is about the right age and was born in Tyrone but do not know if there is any connection: