I know I am replying to an old message and perhaps by now you have found your William ALLISON answers. This caught my eye for two reasons. First the ALLISON surname which links to a family that I share very close Ydna with although they are not of my same surname.
And secondly because of the mention of nearby Limavady in Co. L'derry, Nor. Ireland.
I now believe that I am related to the MOODY's of the Limavady area and our earliest known Moody ancestor was one Thomas MOODY b.c1710 (or there abouts) in or near Agadowey or Aganloo (spelling?) or somewhere near Newtown Limavady.
Our Thomas MOODY married Jean McQUISTON daughter of Benjamin and they along with several other families came to New Castle, DE in c1735 but removed to PA briefly and then headed south to Guilford Co., NC.
Anyway, we have an Andrew ALLISON who had a son Thomas Allison and they were in the Lancaster Co., PA area in the mid 1700's. These Allison's intermarried with GILLISPIE's and they too removed south into Rowan Co., NC which is near where our Moody's were living in Guilford Co., NC.
I believe these Allison's also came to Nor. Ireland from Scotland.
Any connection that you might be able to tell? This is all the info I have on them.