If you look on Irish Ancestors on the website johngrenham.com and do a surname search most Davisons came from Northern Ireland. County Antrim and County Down in particular feature highly with this surname. These two counties are on the north east coast of Ireland, to the north west of the Isle of Man, so your Davisons may have come from this part of Ireland. People with this surname in Ireland are most likely to come from a Protestant background. Their Scottish ancestors settled in Ulster (the north of Ireland) in the 17th century. Irish research for the first half of the 19th century and earlier is difficult due to the lack of online records.