This is what I have on Isreal COLE. Like you, I am stopped right here. I have his ancestors but I cannot connect him to his son ISREAL.
Good hunting
Mel
Israel born 8 June 1653; died 21 Jan 1723/4; married 24 Apr 1674 Mary Paine, widow of James Rogers; born about 1650 Eastham MA; died after 2 Oct 1706 Eastham MA; daughter of Thomas Paine and Mary Snow. His will proved 23 July 1724 and inventory listed his worth at 10,000 pounds
Mary Paine was born in 1652 at Eastham, Barnstable, MA. She was the daughter of Thomas Paine and Mary Snow.
Mary Paine married (first) James Rogers, son of Lieut. Joseph Rogers, on 11 January 1670/71; Eastham.
Mary Paine married (second) Isreal Cole, son of Daniel Cole and Ruth Chester, on 24 April 1679; Eastham. Mary Paine died before 1724 at Eastham, Barnstable, MA; 1710 .
Children of Mary Paine and James Rogers:
1. James Rogers (30 Oct 1673 - 1751)
2. Mary Rogers (09 Nov 1675)
3. Abigail Rogers (02 Mar 1678/79 - 02 Mar 1678)
Children of Israel Cole and Mary Paine:
Named in will of Israel dated 20 Jan 1723/4; (*);
1. Hannah born 28 June 1681; died 23 Feb 1716; married 4 Nov 1703 Samuel Higgins born 7 Mar 1676 Eastham MA; died 10 Dec 1761; son of Benjamin Higgins and Lydia Bangs.
2. (*) Israel born 28 June 1685 Eastham MA; married about 1710 Mary Emery. His will proved 9 Sep 1747 Eastham MA.
3. Isaac born about 1687 Eastham MA.