Hello,
I, too, am researching the Cunningham brothers who left Roscommon, Ireland in either 1761 or 1769. I have found records that indicate both dates. The 1916 book, "History of Nova Scotia" says that they probably came in the spring of 1761 when Richard was a young boy (13-ish?). Wikipedia has an entry for John Cunningham, a Nova Scotia judge, that also has them arriving in Halifax in about 1761. This account says that he married Elizabeth Rust and was commissioner of Indian Affairs from 1769 to 1774 and later in 1783 was Superintendent of Indian Affairs and a judge in athe Inferior Court of Common Pleas in 1778. Since there is clear record (posts in the Halifax newspaper) of two people being whipped for theft from John Cunningham on June 6, 1769 and in that same newspaper, but an edition from earlier in the spring, the weather was reported as particularly bad, resulting in the harbor being closed for a period of time, it seems more likely that the Cunninghams and their group actually arrived in Nova Scotia in 1761 instead of 1769. All I know of their parents is that their mother was named Elizabeth. We have often conjectured that their father died (or perhaps was imprisoned??) and that was what caused the family group to go to American/Nova Scotia.
As to the exact location from which they came, all I've been able to find is that they came from Roscommon. I was there a couple of years ago and learned that that was a place where many of the Scotish people settled and were soon known as Scotch-Irish before many left in search of religious freedom.
I plan to go to Nova Scotia this summer and hope to learn more. If you find more information, I would love to learn of it!
Sincerely, Kate