I've no knowledge of the individuals named however I can think of two general points from my own experience:
John McPartlin, although born in Scotland, was most probably born to parents from the area to which he returned. This happened in my own family.
Have you checked the ScotlandsPeople website for his birth record and census results?
The Beirne/Burns and McPartlin/McPartland names are common in Leitrim too and it may be the case that the families lived nearby but on each side of the Sligo/Leitrim border. Maggie could be from Leitrim and they therefore were married in her parish in Leitrim and lived and had children in Sligo.
Best of luck.