Heather,
You mention a child born in Londonderry – John Murray 7th July 1869. However his parents didn’t marry till 1886 so I assume that’s a mistake. I did search births in Northern Ireland 1886 – 1900 and didn’t find it. Can you verify the date of birth? Do you know why the family was in Londonderry? Was it work, or did they have family there?
Patrick Murray’s marriage certificate in 1866 tells you that his father (James Murray) was dead, but that his mother (Bridget McCormick) was still alive. So if you can narrow the search area, you may be able to search for Bridget’s death 1866 onwards.
Another approach might be to check Scottish Poor Law records. If your ancestors claimed under the Poor Law in Scotland (as many many Irish did), then the Poor Law file usually records their parish of origin in Ireland as well as details of next of kin there. Poor Law records for the Glasgow area are kept in the Mitchell Library. They will normally do a look up for a small fee. You might want to contact them:
http://www.glasgowlife.org.uk/libraries/the-mitchell-library/archives/collections/poor-law-archives/Pages/default.aspx
I do see a marriage between a James Murray and Bridget McCormick in Duneane RC parish, Co Antrim on 15.2.1839. I see 5 children born to that couple between 1841 and 1852 but none was named Patrick, so I am far from certain it’s the right couple. (The children were Francis 24.7.1841; Anne 27.11.1842; Bridget 6.4.1845; James 13.4.1847 & Margaret 30.8.1852). The RC parish records are on-line free on the National Library site:
https://www.nli.ie/en/family-history-introduction.aspx
