Hi Don,
Thanks for your message.
Have you tried using Griffith's Valuation to ascertain whether there were Galbraiths still living in the area in the mid 19th century? You can search this land record online here: http://www.askaboutireland.ie/griffith-valuation/
You could also try checking the 1901/1911 census records to see if any remained there at the turn of the century.
http://www.census.nationalarchives.ie/search/
Unfortunately, Catholic records for the parish do not begin until 1853:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Antrim&parish=Ballymoney&churchid=395
However, Church of Ireland records generally tend to have an earlier start date so if they belonged to this church you may be able to find some information about the family in these records. Most surviving Church of Ireland records are still held by the local clergy, although some are in the National Archives of Ireland and others are in the Representative Church Body Library in Dublin. Here are their websites: http://www.nationalarchives.ie/ and http://ireland.anglican.org/about/42
Lists of these surviving registers can also be found at the National Library of Ireland.
Some other websites which may prove useful are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The National Archives UK ? genealogy search: http://www.nationalarchives.gov.uk/records/looking-for-person/
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Genealogy links: http://www.genealogylinks.net/uk/ireland/antrim/index.html
Family Search: www.familysearch.org
You could also try contacting the Ulster Historical Foundation for assistance, however a fee may apply. Here is their email: enquiry@uhf.org.uk
I hope this is helpful. Please be patient - as our programme has only begun to rollout across the island of Ireland and volunteers in some areas may not yet be organized.
Kind regards,
Genealogy Support