Do you have a location in Nova Scotia? There was no central record-keeping system in the settlements at that time, so it helps to have an area to search in.
Generally, I can find Williams, but there seems to only be one Williamson in my grasp: Sarah (Williamson) Wilson moved from Londonderry Ireland to Pictou NS with her husband about the year 1820. I can speculate that maybe other Williamsons came with them, or followed? Vital Records show Williamsons in that area later in the century, but those records don't go back far enough to help.