Hi James
One of the main hurdles in researching Beith relations is that there aren't many pre-1855 Marriage and Death records for that parish. And there were a number of Kings floating around. If it helps to make sense of them, here is a brief summary of what I've found:
James King & Ann Fulton had 4 children:
Margaret (born 1765 at Gree)
John (born 1767 at Gree, married Mary Cunningham, it seems he took over Gree from his father)
Robert (born 1768 at Gree, married Mary White)
Isobel (born 1770 at Low Gree)
John b1767 & Mary Cunningham had 8 children:
James (born 1810, he might be the James at Burnhouse, Joiner in 1841 Census)
John (born 1812, married Frances Cunningham, he in Dunlop Village in 1841 & 1851 Census)
Robert (born 1814)
Margaret (born 1817)
Andrew (born 1822)
Jean (born 1825, married Archibald Stewart)
William (born 1829)
David (born 1831)
Robert b1768 (possibly) & Mary White had 10 children:
James (born 1802 at Langton, married Margaret McIntyre)
Thomas (born 1804, married Agnes Frame, he inherited Giffen Castle Farm from his uncle Thomas White, died 1860)
Jane (born 1806, spinster, died 1883)
John (born 1809, married Elizabeth Doak, died 1894)
Robert (born 1812)
David (born 1814, died as infant)
Ann (born 1816, mother of William Young)
David (born 1818, went to St Mary's, Perth, Ontario, Canada, married Elizabeth, died there 1877)
Hugh (born 1821)
Mary (born 1823)
James, when your father visited Beith, was he by any chance made aware of any King family headstones? These are a possible source of info which I haven't yet managed to get access to.
Regards
John