Archibald Moore

Archibald & his wife’s marriage and the baptisms of the 2 daughters were long before the start of statutory registration (1845 for marriages and 1864 for births). So you need to rely on church records.

Tradition was to marry in the bride’s church. Both daughters married in Lissan Church of Ireland.  Consequently that’s where I’d look for their baptisms and you may hopefully get their mother’s name from that. Lissan's baptisms start in 1753 (with a few gaps) and marriages in 1744 (likewise with a few gaps). There are copies in PRONI in Belfast. The records don’t appear to be on-line anywhere. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net

Archibald’s marriage might also be in those records too, though if his wife was from a different parish or of a different denomination, then it may not be there. 

I see from his death certificate that Archibald was a labourer. Many labourers couldn’t afford a gravestone so there's a fair possibility that he is in an unmarked grave.

Regarding other children, what I suggest you do is search the marriage records on the irishgenealogy site.  You could search all Moore marriages say 1855 to 1870 in the Magherafelt area. (There’s 34 but you know tow of them already). Check each one looking for men and woman whose father was Archibald and a labourer. That may throw up a few siblings. Otherwise you’ll need to rely on the church baptism records mentioned previously.