Afraid you haven't given us all the details you have yet.
Parish register? what parish, name of church, names and dates?
Catherine Coyle married in Scotland? when did the marriage take place? what information is on her death certificate?
A quick search of IGI finds at least 6 children (could be others- see what you mean about Eliza's surname):
James Coyle & Eliza:
1. John born 29 Mar.1865 Aughnacloy dist., Tyrone (mother- Goolden)
2. James born 31 Mar.1867 Co.Tyrone (mother- Goolding)
3. Margaret born 8 JUne 1869 Ireland (mother- Gouldan)
4. Patrick born 19 Sept.1872 Ireland (mother- Golden)
5. Minnie born 6 Feb.1877 Ireland (mother- Gouldin)
6. Sarah Ann born 22 Jan.1879 Belfast, Antrim (mother- Goulding)
LDS site is free and one of the first places you should look for information. If you've already found above details it helps if you mention that in your post so people don't look for information you already have.
If you are trying to find other living relatives (hopefully also interested in family history) you could try posting on some of the surname boards like Genforum, Rootsweb. etc. if you haven't done so already.