Good afternoon and welcome to Ireland Reaching Out!
As you can see from the link below, Broughshane is in the Civil Parish of Racavan in Co. Antrim:
http://www.irishtimes.com/ancestor/fuses/townlands/index.cfm?fuseaction=TownlandsInCivil&civilparishid=344&civilparish=Racavan&citycounty=Antrim
Records for the corresponding Roman Catholic Church of Skerry or Braid begin in 1825 with some missing dates for baptisms between September 1856 and February 1864 and marriages between September 1832 and October 1878. There are some places where you can search online for records of David and Eliza. However these websites do not have complete collections and many do not cover the period after 1900:
www.familysearch.org has a huge database of genealogical records including some church records for Ireland.
www.rootsireland.ie have a large collection of Irish Church records, however you have to pay to use this site.
http://www.ancestryireland.com/ The Ulster Historical Foundation has some gravestone transcriptions that you can search for free for Co. Antrim
Other important sources include the Tithe Applotment Books and Griffith?s Valuation. Even though these sources only record the head of the household, the information is very important and can be valuable:
Tithe Applotment Books (1823-1837): http://titheapplotmentbooks.nationalarchives.ie/search/tab/index.jsp
Griffith?s Valuation (1847-1864): http://www.askaboutireland.ie/griffith-valuation/
The National Archives of Ireland: http://www.census.nationalarchives.ie/search/ you can search the 1901/1911 Census on the National Archives page too, for instances of the family name at that time
Remember to post any new information that you find here. The more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.
Best of luck with your search
Clare Doyle
Genealogy Support