Many thanks for all of the information which I will look into. It is so difficult to prove a link. I have all family members from Thomas and Mary up to the present time but can't seem to prove a link with any of the William Coates I have come across. Some of William's family it is said disowned him for marrying a Catholic. I have not come across any other children of William and Margaret, only Thomas. My father always said that there was a lot of land belonging to the Coates in Ireland.
Thank you again for your help.