Shirley-Ann,
The surname is not a common one in Co. Leitrim. In the 1901 census there is just a single Darling family, they were farmers in Druminshin Glebe, which is in the parish of Carrigallen.
http://www.census.nationalarchives.ie/pages/1901/Leitrim/Carrigallen_West/Druminshin_Glebe/1476270/
The above William died 9.6.1904.
There’s no-one named Darling in the county in the Griffiths Valuation records for 1857 (though that only lists heads of household. People with very poor properties, servants and those sharing houses wouldn’t be listed). There are no Darling households in the tithe applotment records for the county either (1823-37). Again that’s not conclusive, as you would only be listed if you had land. Labourers etc weren’t listed.
Statutory birth registration only started in Ireland in 1864 so you won’t find a birth certificate for Anna Maria as its too early. But that would allow for a siblings birth in 1865 to show up in the stat records.
You don’t say what denomination the Darling family were, but I would guess Church of Ireland (as most Darlings in Ireland in the 1901 census were that denomination). If the family did come from Drumreilly parish, then the bad news is that those records were lost in the 1922 fire in Dublin.
You say that Anna married twice and then died. Do none of those 3 certificates contain her parents names?
I did find the marriage for William Darling and Eliza Arnold. That was registered in Mohill, Co. Leitrim in 1949, Volume 8, page 156. It might be worth ordering a copy of that to see if you get any clues from it. You can order a photocopy of the civil certificate from GRO Roscommon for €4 (euros). http://www.welfare.ie/en/Pages/Apply-for-Certificates.aspx
You have to download and print off the form. Then either post or fax it back to them. You can’t e-mail it to them. However if you want them to e-mail the cert to back to you, they will do that, so tick the relevant box.
Tradition was to marry in the bride’s church which should be on the certificate (unless it was a Registry Office marriage). That church may be the place to look for her baptism and that of any siblings.
Catherine’s birth in 1865 was in the townland of Drumshangore. (Newtown Gore is where the Registrar’s office was based for that area). Drumshangore is also in the parish of Carrigallen, same as Druminshin Glebe. So the families might be connected. Sadly the Carrigallen Church of Ireland records (which started in 1802) were burned in the 1922 fire.
I do see 2 siblings for Catherine. Samuel was also born to the same parents at Drumshangore on 20.11.1867. Ralph was born in 1871. His mother, Eliza Darling died on 14.10.1891 aged 66. Husband William died on 13.2.1884 aged 71. Both William and Elizabeth left wills. She was his executor but her executor was her son Ralph. Not sure if either will survived the 1922 fire but you could enquire:
http://www.willcalendars.nationalarchives.ie/search/cwa/home.jsp
There were no Darling households in Drumshangore by 1901:
http://www.census.nationalarchives.ie/pages/1901/Leitrim/Corrala/Drumshangore/
I searched for Ralph, Catherine & Samuel in the 1901 & 1911 censuses but did not find any of them. I also searched for their deaths 1864 to 1901 but found none. That suggests they may all have left Ireland.
So if the family came from either Drumreilly or Carrigallen, Anna’s birth is too early for a stat birth certificate and the church records are destroyed. No easy way forward from that. But if you can get her parents names from one of the Australian certificates that may help.You might also want to search on Ancestry for migration records for the 3 siblings, and perhaps in the English & Scottish 1901 & 1911 censuses in case that's where they went.
