At your stage, there is really only one port of call, and that is Scotland's People (SP).
I think if I were you I would go to
www.scotlandspeople.gov.uk, put Culhane in the search box on the home page, and see what turns up. You can look at the indexes for free, but to view the original documents you need to buy credits.
Unfortunately there aren't nearly enough Culhanes to account for six children in Glasgow, so I suspect that at least some of them must have spelled their names in other ways, which makes life awkward. Or they might have retired home to Ireland.
I tried using c*lh*n*, and got a lot more results. I looked at the deaths, and there were 109. Restricting it to people who died after 1914, and who were aged at least 40, reduced it to 33, which is manageable. You can then go through the list and eliminate any who are too young to be Catherine's children, and take a look at the rest.
Catherine's own death certificate is available to view at
https://www.irishgenealogy.ie/en/ but unlike Scottish death certificates, Irish ones don't usually tell you the names of the deceased person's father, mother and spouse(s). She died on 25 January 1914 in Rathkeale Workhouse. Her age is given as 91, and she was from Ballinacarriga (I think - it's hard to read). There are also 8 deaths of James Culhanes registered in Rathkeale, but the images of 7 of them are not yet available online. The 8th one was registered by his wife, whose name was Ellen. I can't find Catherine in the 1911 census at
http://www.census.nationalarchives.ie/search/.
There are 42 marriages of Culhanes registered in Rathkeale - you might like to have a look through those (though the images of the earlier ones are not yet available) to see if any could be the children of James and Catherine, and then check the Scottish census to see if any of them moved to Scotland after marrying.
Hope this helps. Any questions, just ask.
PS I just took a look at the article in the
Queensland Times. I wonder whether it actually means that there is just one son in Glasgow, who has six children? I took a look at the death certificate of Patrick Culhane, who died in Greenock in 1908 aged 67, and he is definitely the son of James Culhane and Catherine Murphy. His wife Helen (nee Allan) died in 1909.
The 1901 census lists Patrick Culhane, 59; Helena, 58; Maggie, 26; John, 23, Helen, 21; and William, 18. You can view the original of this, which will tell you their occupations and birthplaces.
There are births of Ellen, 1871; Margaret, 1874; John, 1877; Helen, 1879; and William, 1882, all in Greenock. Ellen died in Greenock in 1874, and there is also a death of James, aged 17, in Greenock in 1887. So it looks as if the family came from Ireland after the birth of John in 1869/70 and before the birth of Ellen in 1871.
Or maybe not. In the 1881 census they are listed as Culhean. Patrick, 40; Helen, 38; James, 12; Mary 16; Catherine, 14; Margaret, 7; John, 4; Helena, 2. Parents born in Limerick, first three children in Port Glasgow, the others in Greenock.
The IGI at
www.familysearch.org gives birth dates for Mary (Culhene), 11 March 1865; Catherine (Colhane), 8 March 1867; James, 25 February 1869; Ellen, 14 May 1871; Margaret, 21 January 1874. The IGI stops at 1874 so John, Helen and William aren't included. That's a total of 8 children, less two who died, leaving 6 alive.
The birth certificates of the children will tell you the date and place of their parents' marriage.
