Wow, so many first or last names are similar, but alas, not the timeframe.What geography do you have associated with your McBurnie and Mulligan?Part of my line came from Ballynahinch, IR and settled in western Pennsylvania.
Here are names of part of my family's story:
Jeanett Milligan married James McBurney in 1762.
Their son John 1764-1846 married one of the enigmas of our family, Sarah Hunter 1774-1863.
Their daughter Esther 1799- married a R. Donaldson.Their daughter Jane 1793-1866 married Andrew Donaldson 1789-1843.Jane and Andrew were married, September 20, 1814.My main interest is with this branch.