According to the seanruad site, Churchland Quarters is in Co Donegal and consists of 5187 acres in Donagh parish. Like quite a few places in Ireland it has alternative names, such as Carrowtemple, Moneyshandoney & Carrick. You can see where it is by using Griffiths Valuation maps or on this website;
https://www.logainm.ie/en/s?txt=Churchland+Quarters&str=on
It’s around the town of Carndonagh. In the 1901 census it had a population of 705, in 154 households:
http://www.census.nationalarchives.ie/pages/1901/Donegal/Carndonagh/Church_land_quarters/
I don’t see Ballibranigan on Griffiths maps, as any part of Churchland Quarters. Over the years many townland names and sub-divisions of townlands fell into disuse. Perhaps someone with local knowledge may be able to help but if Ballibranigan’s not been in use for several hundred years, it may be hard to locate. (Few detailed local maps exist prior to the OS maps in the 1820s).