I think you meant 'dairy farmer' but 'fairy farmer' sounds much more interesting

It more likely that Bernard McPeake had what is called a mixed farm- in those days he would have had a cow or two, some pigs, chickens, etc. & grown a variety of crops on probably 10 or less acres (oats, potatoes, turnips, etc.). It's really only in the last 30 years or so that farmers have become more specialised.
I tried to find what records are available for St. John's Church, Swatragh buit this was the closest I could find- hopefully someone else will be able to give more detailed information.
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Derry&parish=Maghera&churchid=374You've said 'Swatragh area' so it sounds as though you don't know the exact townland?
The only Bernard McPeake I could find in the wider area in Griffith's Valuation was one in the townland of Derrygarve (Artrea Parish, 1859) but perhaps the property would have appeared in someone else's name in the mid-1800s.
It may be difficult to get back another generation since that period is well before the start of civil registration.