There is a Cates cemetery on Welch Whitfield Rd, behind a house. There are only 3 burials here.
C C Cates, his wife Kate, and Mary who was wife of J M Chandler.
We were told there used to be a cemetery (with Brooks) across the street in a field, but the fieldstones, which were in the water way, have all been removed by farming. It is my understanding that the people were not moved. That may be where your folks are located. I would suggest doing some research on land records to get any further information.