White & McAllister G.Grandmother was asaour

Ballycastle Golf Club is in the townlands of Bonamargy and Broughanlea, both of which are in Culfeightrin parish. I can’t identify a farm named Hillhead on an 1860s map of the area.

Looking at Griffiths Valuation for 1861 there are no White or Kyle households in Bonamargy, but there is a Robert Kyle in Broughanlea who had plot 5a which was a 16 acre farm.

http://www.askaboutireland.ie/griffith-valuation/index.xml

His descendants were still there in at least 1901:

http://www.census.nationalarchives.ie/pages/1901/Antrim/The_Fair_Head/Broughanlea/922126/

The family were Presbyterian (so of Scots origins). Nearest Presbyterian church was Ballycastle whose records start in 1829. So if the White family were also Presbyterian you might find William Patrick’s baptism there too.  But you will obviously struggle to get back much further via church records as there aren’t nay. Ballycastle’s Presbyterian records have been copied and are in PRONI, the public record office, in Belfast. They are not on-line there and a personal visit is require dot view them. (So you might need a researcher).

There was another Presbyterian church not too far away in Ramoan but its early records were all lost in a fire.

Looking at the 1803 Agricultural census for the area, there were no White households in Culfeightrin. There was one probably Kyle family in Broughanlea. That was headed by Denis Cawel (which seems a variation of Kyle to me).

Local gravestones might throw up a bit more information.