Bishop Colin Falconer's family is traced in my book, _Falconer of Halkerton_ (Heritage Books, 1997), now out of print.He was the son of William Falconer in Lethinbar (b. c.1600?, d. 1644-1649), by his wife Beatrix Dunbar (d. 1681), daughter of J. Dunbar of Bogsmoray and widow of Patrick Dunbar of Haldoch.
William Falconer in Lethinbar was the son of William Falconer in Logie and in Dunduff, who was living in 1616 but dead by 1625, and an unknown mother.
The last William was the youngest son of Alexander Falconer of Halkerton (b. c.1522, d. 10 Nov. 1587 at Lethen, Nairnshire), and Elizabeth Douglas, daughter of Archibald Douglas of Glenbervie by Agnes Keith, daughter of William Keith, 3rd Earl Marischal.
There are many lines to Robert III, King of Scotland, from this couple. My suggestion would be that you look at Sir James Balfour Paul, _The Scots Peerage_ (Edinburgh: David Douglas, 1908), which is at many research libraries, to trace all the lines---there are too many to list here.
It seems that the only descendants from Colin are through the Innes family and I was interested to learn of the immigrants to Virginia.