Hi, I'm glad you were able to find some new info, and happy to say I may have something for you.
I found the following entries.
James Kilgour and Katherine Reid of Falkland - Katherine born Nov. 8, 1789 - Barbara born Oct. 30, 1791
These are the only two entries I could find for births of their children.
I then did a search through trying to find a birth for your James Kilgour and found: William Kilgour and Barbara Forbes - son James born Nov. 29, 1773
This seems very likely to me as your James and Katherine seem to have named their second daughter Barbara and the Scottish tradition was for parents to name first daughter after Mother's mother, second daughter after Father's Mother.
Other children of William Kilgour(listed as a cooper) and Barbara Forbes were: William, born Nov. 27, 1768 Elizabeth, born Nov. 4, 1770 James, born Nov. 29, 1773 (above James) Barbara, born March 19, 1786 Looks like a big gap there between 1773 and 1786 so I went back and double checked both my record and my Dad's record(we had independently covered the same microfiche for these records) and we both have that date as shown.
I also found the following entries that I thought I would give you as they may tie in with your family. I think John and Agnes "may" be in my family as well, but have no real proof, just the way the naming of children was done---fits!
John Kilgour and Agnes Reid David, born April 6, 1829 Agnes, born Nov. 6, 1830 James, born Feb. 10, 1833 Isabella, born June 23, 1835 Elizabeth, born Oct. 25, 1837
I'm sorry that I can't help you out with Katherine Reid's birth as when I copied the records I wrote down all Kilgours. I just didn't have time to copy the whole set of records........... wish I had though.
Let me know if I can be of any more help ***as you are in Canada I am wondering if you have any information on the Kilgours that went to Brandon, Manitoba, in the late 1890's or early 1900's?? I was told my gr-grandfather's brother came to Brandon, while my gr-grandfather came to Vancouver. My grandfather first went to Manitoba, then on to Vancouver. As he came when he was only 16 I suppose he may have gone to stay with his uncle before the rest of his family came over. Just a thought.