Just to note the following until you can rule in or out.
From the 1864 civil marriage record you should know that William O'Neill's address was the townland of Drummuck in the civil parish of Maghera, if that's where his parents lived (there's no guarantee, William could have moved to Drummuck shortly before the marriage), there is a possibility for his father in Griffith's Valuation in the form of a Francis Neill living in Drummuck in a house with just over 2 acres of land (the local print date was 1859):
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearchAgain speculative, but a possible sibling James O'Neill was baptised in Termoneeny RC parish in 1838 (6 May?) for parents Francis O'Neill and Peggy McMullin, the address was Drummuck (right page, 3rd baptism up from bottom):
http://registers.nli.ie/registers/vtls000633051#page/14/mode/1upA James O'Neil with an address of Drummuck and father given as Francis O'Neil, a farmer, married a Sarah O'Lone in Lavey RC Church on 13 November 1870, the couple went on to have a number of children and can be seen here in the 1901 Ireland census:
http://www.census.nationalarchives.ie/pages/1901/Londonderry/Gulladuff/Drummuck/1544794/As I said, speculative, so just to note in case it offers up leads.