I have a Charles McAllister in my family tree who married Eliza Wightman (Circa 1779 - July 1885) daughter of John Wightman 1752 - 1801 and his 1st wife Margaret (May or Eliza) Kennedy ? - 1780 they had a son Rev Charles James McAllister (1810 - 1891) and another son John is mentioned in letters Nancy and James Wightman wrote home to Lisburn, Ireland from America, which can be found on the Irish Emigration Database (IED).
This information is a little convoluted and it has taken me weeks to research and sort everyone out, as I think the information on the one page is from 2 different sources and they call some of the same people different names.
There is also information on a George McAllister marrying Elizabeth Henderson on IED under "Family History of the Wightman and Henderson Family, Co Down"