Very interesting.
That first baptism for Margaret Branigan has my 2x great grandfather Michael Morgan who lived in Cornamucklagh North, Clontibret, Monaghan when the Griffith Valuation was completed in 1860 as a sponsor. He was married to Ann Branigan in Keady/Derrynoose, Armagh in 1849, but appeared to move back to Cornamucklagh North to farm around his Branigan family around 1860. Morgan's were from townland Croghan, Clontibret, Monaghan and baptised one of their children there in 1863. If these are your Branigan's they are tied to the townland Annagh, Monaghan Branigan's all around St. Michael's church in Annayalla, Clontibret, Monaghan.
They do spell the name Branigan and also Brannigan. It is documented both way in family bibles in my family.