I used to live in Monument Beach and did some research for another member of your family. You have several lines to Nantucket too which connect you to the earliest Nantucket whaling families through Abraham Hoxie's marriage to Charlotte Pinkham. If you have further interest in the genealogical work I did for the Cunninghams, I'll willingly share.
I also did work on Eldon (?) Cunningham's wife's people who came (as I recall) from New Hampshire.. but I don't have the notes at hand and I may be off on that.
Your original Cunningham ancestor (whom I believe died in Bridgewater, Masschusetts after his immigration from Ireland) was, as I recall, the father (I don't have his first name at hand) of George Cunningham who married Rebecca L. Hoxie. Copy and paste the link I provide at the bottom into your browser and go to the line of Abraham Hoxie, then to daughter Rebecca L.http://freepages.genealogy.rootsweb.ancestry.com/~hoxieschen...