I do not know if this is the family you are looking for, but this story goes with the family Chris mentions:
Daniel Cunningham was born in 1731 in Dublin, Ireland. His middle name may have been David. Some sources list his mother as Bridget Dolan. He came to the USA about 1743. Sources tell us that the family emigrated to Canada in 1795. The Revolutionary War ended in 1783 and Daniel died in the Richmond Virginia jail in 1798 therefore I am not sure that Daniel went to Canada or just his family. Three of Daniel’s grandchildren and their families emigrated from Canada to Central Nebraska. Martha’s Cunningham’s son, George Bull and family left Canada in 1869 and Stephen’s son, Paul and family left in 1870 and Stephen and family followed in 1871.
The following history was taken from the book “Pioneer Life on the Bay of Quinte”. .....continued