This site is a collation of descendants of Archibald Allison of Ireland or Scotland.
The information comes from various Allison descendants, both in my line and others.
Some genealogies list Archibald as an Irishman, arriving from County Monaghan. Others indicate he was an Ulster Scot, originally from the Avondale area of Scotland — these two claims are, of course, not inconsistent with each other — but they indicate no source for this information. However, his wife was Mary Allison née Kennedy of Kirkmaiden, Scotland and there is a family bible in the possession of Mrs. G. C. Kling of Lock Haven, Pennsylvania inscribed "Property of Mary Kennedy Allison of Kirkmaiden, Scotland." I tend to think this implies her residence in Scotland after marriage rather than just her birth place. Given how common the name Archibald was in those days among the Allison family of the Avondale area, I believe there is a reasonable case for a Scottish birth.
Verna Allison Pierson and Marlowe G. Smith, in their unpublished The Allisons of Centre County, Pennsylvania, trace our Archibald1708 back through an Archibald Allison (b. 1689) to the Covenenter, Rev. Archibald Allison (b.1656), who was martyred at the Grassmarket in Edinburgh in 1680. I've seen no indication of this link in other sources and [Pierson/Smith] has been inaccurate in several places. While it's credible that Archibald1708 might be related to Archibald1656 if they were both from Avondale, the problem is that Archibald1656 was executed in 1680...about nine years before Archibald1689 was born. Therefore, I tend to think direct ancestry is unlikely and have elected to start this genealogy with Archibald1708. Leonard Allison Morrison, in The History of the Alison or Allison Family in Europe and America, lists Archibald1708 but does not tie him to the Scottish Allisons, saying only, "...who migrated from the county of Monaghan, Ireland, in 1783, and settled in Centre county, Penn."