You need to read a book called the Descendants of Elisha Cole. Daniel and Susannah Ogden Cole are mentioned in this book.
My Cole line was also in New York and moved to Michigan, but I have found no evidence that they are related to my line.
As far back as I have been able to ascertain, I am investigating an Elder John H Cole. He lived in Springwater, Livingston County which was part of Ontario County at one point. My 4x Great Grandfather was born in the area when it early 1812. All my leads are pointing me to this man as his Father.