William and Robert Boyd were brothers and lived in County Antrim, Ireland. Robert and William were members of the Covenanter Church of Scotland. I do not know any specific history of William and Robert except that William came to American as part of the Rev William Martin migration in 1772. Martin was a Covenanter Minister at Kellswater, County Antrim. There were 467 families (over 1200 people) who made the journey with Rev. Martin. According to Stephenson, they were from the areas of Ballymoney, Ballymena and Kellswater in County Antrim.1
Nothing is known about these specific Boyd's in Ireland. Since William was a farmer after coming to South Carolina, as were his descendents for several generations, it may be assumed that the Boyds in Ireland were also farmers.
1 Jean Stephenson, The Scotch-Irish Migration to South Carolina, 1772 (Rev. William Martin and His Five Shiploads of Settlers), Washington, DC, 1971, reprinted for the Clearfield Company: General Publishing Co., Baltimore, MD 1999 - 2008, ISBN-13:978-0-8063-4832-2 and ISBN-10: 0-8063-4832-1