Quite a bit of information online for your family at Ancestry.Starts with Robert Barnhill b. 1703 in Ireland, to son Samuel Barnhill b. 1732 in Ireland, to son Daniel Barnhill b. 1771, to son James Barnhill b. 1797, to son James Sylvester Barnhill b. 1837, to son Hugh B. Barnhill b. 1872, to daughter Elsie F. Barnhill Pettyjohn b. 1899.
This Barnhill family migrated from Ireland to PA, SC, KY, IN before settling in Liberty, Marion Co, Iowa and are found on a number of censuses and was pretty easy for me to track.
Made some copies of the censuses if you don't have access to Ancesty and would be happy to give you more information if you would like?
Samuel Barnhill b. 1732 was the brother of my line, William Barnhill b. 1733.