By process of elimination the parents of Andrew Canagh would seem to be Andrew Canagh and Elizabeth.
Rootsireland.ie shows:- Andrew Kanna and Elizabeth Brady married in Glendalough (RC) in 1843.
With these parents, there was an Andrew Canna baptised in Glendalough (RC) in 1849. Other children baptised in Glendalough (RC) with mothers surname are:
Thomas 1844
Margaret 1846
James 1849
Patrick 1852
Children baptised with only mothers forename in Glendalough are as follows:
Ambrose 1844
Bridget 1846
James 1851
Christopher 1842 ?
Andrew 1849
William 1862 Rathdrum (RC)
It would seem that there may be three sets of twins if these records are correct and match your Canna Family.
As shown earlier by Shane, Thomas Canagh married to Bridget Kearns in Kilquade (RC) 1868 has same parents as Andrew.
Familysearch.org and Rootsireland.ie show their children as follows:
Christopher 1869
William 1870
Mary Jane 1873
Eliza 1875
James 1879
Bridget 1883 All baptised in Kilquade (RC)
Another brother of Andrews is Patrick married to Catherine Grogan in Kilquade (RC) IN 1868 GRO INDEX VOL. 12, PG. 781.
Patricks parents as above.
Children for this couple:-
Ambroise 1868
Catherine 1872
Christopher 1876
Patrick 1879 All baptised in Kilquade (RC).
As suggested by Shane and PM, start with the Marriage Cert and perhaps the Parish Record for Andrew and Philomena. Have a look at these enteries and hopefully they match your Canna Family.
Wicklow way