This is what I found............
Going (Traverston & Violethill) | Landed Estates | University of Galway
In the Tithe records a Robt (Robert) Goins Esq was in County Limerick.
The Tithe Applotment Books, 1823-37 (nationalarchives.ie)
The Townland is Fairyhall. this is just over the Tipperary Limerick border.
Fairyhall Townland, Co. Limerick (townlands.ie)
on here............ page 2 you will see Robert in Fairy Hale but all the other names in the same area.
The Tithe Applotment Books, 1823-37 (nationalarchives.ie)
From this information
Where they Catholic?
If they were, use
Catholic Parish Registers at the NLI
Then Castleconnell and Newport Parishes.
After that you use births from 1864 marriage from 1844. Deaths if they are there. (Most are now)
Welcome to Irish Genealogy - Irish Genealogy
If non Catholic one of the other helpers on here uses Rootstireland and that has many Religions.
I have looked at the ANCESTRY names for travel to Australia and cannot see any Goins Going or the Colemans you name.
Your TROVE site will have that information.
Then back track from the information you get from there.
Cheers
Margot