No evidence has been provided that John Cooper's parents were Thomas Cooper and UNKNOWN UNKNOWN so they have been detached from this profile.
Jacobus tells us only that John Cooper died in New Haven Colony on November 23, 1689; he went by the title 'Cpl.'; his first wife and mother of his children was ____, and his second wife was Jane Woolen, the widow of John Hall.
There was a John Cooper who came on the Hopewell in 1635, and settled in Lynn, Massachusetts, and later Southampton. That was a different John Cooper from the one who settled in New Haven.
JOHN COOPER  immigrated to Lynn, Mass. on the "Expedition" in 1635.
He subscribed to the New Haven Fundamental Agreement on June 4, 1639. In the same year, he was an agent for the Iron Works. He was admitted a freeman on Oct, 22, 1645 in New Haven.
He may have had a wife & children in England, and he may have married the daughter of John Woolen, who lived in New Haven but traveled with Lamberton to Delaware Bay to interpret in his dealings with the Indians.
His residence was on the west side of Church Street, at the corner of Grove Street in New Haven. In 1643 his household was comprised of three persons and an estate of 30 pounds which included nine acres of upland, 1 1/2 acres in the Neck and 3 acres of meadow, plus 12 acres upland from the second division.
John Cooper was mentioned often in the old records. He was appointed to be a "chimney inspector" from 1643 - 1649. Chimneys were one of the leading causes of fire. If the chimney was not clean, he cleaned it and charged the person for his services. He also served as surveyor of highways, constable of New Haven, a pounder of stray livestock, and a townsman for 27 years. In 1644 he was fined for coming late to a meeting with his arms, and again in 1647 for not having a gun rest.
In 1652 John Cooper appealed the verdict of a Southampton jury regarding a bill which was not authentic. In court again in 1655, he was found to have "unjustly molested, grieved, & dissparaged" Jonas Wood, for which he was ordered to pay 40 pounds. In 1659 he was fined 5 shillings for excessive drinking. In 1664 John Scott charged him with "high treason". He was commissioned as Corporal of the New Haven train band during unrest between the Dutch & the English, but he never saw action.
In 1673 he dissented from an agreement on the boundaries of New Haven in regard to the meadow. He signed with his mark, "IC".
He was a deputy to the General Court in Hartford for New Haven for several years.
John Cooper (Thomas) was born in England about 1612 .
Jacobus Families of Ancient New Haven disagrees with this:
John Cooper married three times. He married an unknown person. He married Jane OR Jeanne Woolen. He married Mary Woolen in New Haven, New Haven, Cn. Mary was born bet. 1614 and 1618, in England, daughter of John Woolen. Mary died abt. 1685, in New Haven, New Haven, CT. John Cooper and Mary Woolen had the following children: The children listed are correct but by his first wife.
John m. (1) ____ ____ mother of his children; m. (2) Jane Woolen, widow of John Hall.
Children b. in New Haven, New Haven Colony; bpt New Haven First Church: 
Hannah Cooper was born 1638; bp 15 Aug 1641; 15 June 1675 in New Haven, New Haven, CT, at 35 years of age. She married John Potter about 1661.
Mary Cooper was born 1640; bp 15 Aug 1641; died 4 January 1705/6; m 2 Dec 1658 Abraham Dickerman in Dorchester
John Cooper, bpt. ; died 1708. He married Mary Thompson 27 December 1666 in New Haven. Mary was the daughter of John Thompson and Dorothy Harrison. Mary died November 1714 in New Haven.
Sarah Cooper was bpt. 21 September 1645. She married Samuel Hemingway 23 March 1661/2 in New Haven. Death Sarah died 20 September 1711 in East Haven, CT, at 65 years of age.
John died 23 November 1689 in New Haven, New Haven, CT, at 77 years of age. His body was interred 1689 at the
Center Church on the Green Churchyard, New Haven, New Haven County, Connecticut, USA. Plot: PLEASE READ THE TABLET IN THE REFERENCED PHOTO...THERE ARE NO STONES REMAINING IN THIS CEMETERY (EXCEPT IN THE CRYPT)...THEY WERE ALREADY GONE OR MOVED TO GROVE STREET IN THE EARLY 1800'S. 
↑ Donald Lines Jacobus, "Families of Ancient New Haven", Vol III, page 451 (Cooper Family).
↑ Robert Charles Anderson, “The Great Migration: Immigrants to New England 1634-1635”, Boston, New England Historic Genealogical Society, 1999-2011, Vol II, C-F, page 202.
↑ James Savage, "A Genealogical Dictionary of the First Settlers of New England", Boston, 1862, page 454.
↑ William Richard Cutter, A.M., New England Families, CD-Local and Family Histories: CT, 1600's - 1800's, (Produced in collaboration with the Genealogical Publishing Company, 2000), vol 3, p 1072.
↑ Find-A-Grave: Mary Woolen Cooper, Memorial# 112397124
↑ 10.010.1 Jacobus, Donald Lines (compiler). Families of Ancient New Haven, Vol I-VIII. and Index Vol IX New Haven: 1931. Reprint, Baltimore: Genealogical Publishing Co., Inc., 1974, 1981, 1997. Originally published as New Haven Genealogical Magazine, Volumes I-VIII. (Rome, NY and New Haven, CT 1922-1932). p. 451/2
Information developed from Find A Grave memorial no. 28266354 
Website: John Cooper (1610 - 1689) Part One; Ives Family History Blog - This genealogy blog covers the story of William Ives, co-founder of New Haven CT, and many of his descendents, as well as those who married into the family (e.g., Bassett, Dickerman, Yale, Atwater, Peck, Cooper, Day, Humiston, Bishop, Dunbar, Rich and many others).
It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share DNA with John: