I've taken my research from Wm's notes and used them as a guide.  I have found many parish records, civil records which are online from Ireland,  names in the Wills index, newspaper items, and other sources eg directories.  Wm's notes led me a merry chase and so for a period I put them aside and started again.  I have transcribed this summary from my family history programme. 
Arthur DUNN 1737-1814 was married to Mary UNKNOWN - she died 27 Jan 1787.  Burial recorded in parish records of st James COI, Dublin. There were eight children.  My ancestor Arthur 1761-1792 was the eldest [he married Jane GORDON in 1780] and your ancestor Hester 1764-1796, the youngest. 
William HUNTER c1760-1894 married Hester DUNNE 1764-1896, on 30 July 1785 at St James COI, Dublin.  Four children - John Arthur 1786-1840, Clara Wilhelmina 1788-1861, William 1789-, and James Henry 1790-1830.
John Arthur HUNTER 1786-1840 married Jane Ann Mary GREENE 1798-1880, on 5 Sep 1815 at St Mary's COI, Dublin.  John Elias HUNTER 1825-1895 was their son.  I haven't recorded all their chn.
John Elias HUNTER 1825-1895 married Joanna FITZGERALD 1845-1885, on 27 Nov 1865 Carmoney, Antrim and I haven't recorded all their children however there was a Sarabella [?Bella] HUNTER born 18 Jan 1875  and baptised 18 Mar 1875 in the Parish of Clontarf, Dublin.  Parents John Elias and Joanna.  Father's occupation - in Court of Bankruptcy.
From the marriage registration [certificate] James Hume NELSON, full age, accountant, father John  James T NELSON, seed merchant, married Belle HUNTER, full age, father John E HUNTER, Deputy Registrar, Four Courts, on 5 Jul 1905 at St Patrick's, Monkstown, Co Dublin
Edit to correct groom's father's given name.