To start with, McCaughern (and variations of the surname) is quite common in Rasharkin, Co. Antrim (just across River Bann from Kilrea, Co. Londonderry. It's quite possible your McCaugherns lived on the Co. Antrim side but Daniel married in Kilrea (marriages usually take place in bride's church).
Do you have any idea what religion the family would have been? my first guess is Presbyterian with second choice being Church of Ireland.
PRONI (Public Record Office of Northern Ireland) has a Will for a Daniel McCaughern of Ballydonnelly (Rasharkin area)- "The Will of Daniel M'Caughern late of Ballydonely County Antrim Farmer who died 12 January 1893 at same place was proved at Belfast by John Elder of Lisnagaver said County and Samuel M'Caughern of Ballydonely Farmers the Executors." See
www.proni.gov.uk for more details and Will. Mentions wife Liza Ann, son Samuel. Can't find listing in civil index to see his age at death (spelling of surname likely the problem).
The 1901 census is the first complete census for Ireland but fragments of 1851 for Co. Antrim do survive and there's a Mccaghrin family in Lisnagavor townland (Rasharkin area) which seems to tie into the above Will (all b.Co.Antrim)-
Sarah Mccaghrin, Head, widow, 70
Daniel Mccahrin, Grandson, unmarried, 19, farmer
Sarah Mccaghrin, Granddaughter, unmarried, 17
Margaret Mccaghrin, Granddaughter, unmarried, 12
Margaret Elder, Head, widow, 60, land holder
Esther Elder, Daughter, unmarried, 25
Elizabeth Elder, Daughter, unmarried, 24, Dressmaker
William Elder, Son, unmarried, 22, Agriculturist
There's at least one other family in the census (search for 'mcca' and you'll see them-
http://www.ulsterancestry.com/ShowFreePage.php?id=177