Notes:

Does not appear in the 1850 Census. Married or deceased.

Notes:

The "Barns/Kirkland Cemetery" monument/records indicate that John was married 4 times. The monument was erected after his death by daughter Loreen.
1st - Mary COOK (1791-1815) m.abt.1810-1815
2nd - Lucy ARNOLD (1788-1836) m.abt 1816-1820
3rd - Martha DOUGLASS (1800-1845) m.abt 1837-1838
4th - Eunice STOCKWELL (1795-1883) m.May 14, 1850

[Deeds]
12/27/1816 (Indenture for $50) Lot#5, Cox's Patent, Grantor, Moses COOK.
3/10/1818 (Recorded Lot#5) 1/2 acre, Grantor, Moses COOK.
1818 (not recorded) John purchased 1 acre Grantor, Jesse CURTIS.
1838 John sold 1/10 acre to Kirkland School District.

Note that the property sold by Moses COOK was "after" the death of John's wife Mary COOK and that John was of the town of Paris.

[Will]
I have published the Will of John GREEN online at http://www.rootsweb.com/~nyoneida/ in the "Wills" section. The will lists children Mary (GREEN) TARBOX and Edward C GREEN.

In the 1800 Census of Oneida, only Charles GREEN of Bridgwater and Ezra GREEN of Rome had sons of John and David's age living at home. John's parents had atleast 2 children, David and John. David moved in with brother John sometime after 1840. Listed with John's family in 1850 & 1860 census. Gone before 1870 census. Probably died as he would have been 84yrs in 1870. The family moved from RI to NY between 1786 and 1790 based on 1860 census data from John & David's birth states. This is also backed up with data from the civil war pension records of John's son Gardner stating he was from Kirkland, Oneida NY. Location of residence was found and verified on an 1874 landowners map of Kirkland Town.

[1800 census]
Charles (Bridgewater) 11101-00001
Ezra (Steuben/Rome) 31001-10110

[1810 census] J. Green p.83
0100100002
1 male b.1795-1800 => ?
1 male b.1755+ => J. Green
2 female b.1755+ => ?

[1814 - Town of Paris Index]
I believe that John is my GGG-Gfr and John 2nd is the husband of Mary COOK or Lucy ARNOLD. I do not see this group of Green's prior to 1814 in Oneida. Birth estimates are from cemetery information and links are not proven yet.
Green, John
Green, John 2nd
Green, Jonathan b.1788
Green, Nathan b.1769
Green, Tillinghast
Green, William

[1820 census] Paris p.268 partial match. Kirkland was formed in 1827 from Paris.
010010-200100-001
1 male b.1804-1810 => ?
1 male b.1775-1794 => John Green
2 female b.1810-1820 => Aristeen, Loreen
1 female b.1775-1794 =>Lucy Arnold (wife)

[1830 census] Only John GREEN in Kirkland.
0000110000000-0120001000000
1 male b.1800-1810 => ? (matches in 1820 & 1840)
1 male b.1780-1790 =>John Green
1 female b.1820-1825 =>Mary Ann Green
2 female b.1815-1820 => Aristeen, Loreen
1 female b.1780-1790 =>Lucy Arnold (wife)

[1840 census] Only John GREEN in Kirkland.
1 male b.1835-1840 =>Gardner D Green
1 male b.1780-1790 =>John Green
1 female b.1835-1840 => Lucietta
1 female b.1820-1825 =>Mary Ann Green
1 female b.1810-1820 =>Loreen or Aristeen
1 female b.1790-1800 =>Martha Douglass (wife)

Possible link:
Rome Citizen Death Notices in 1887 - GREEN - In the town of Kirkland, New York, May 2, 1887, CATHARINE GREEN, aged 62 years. (RCMay06/1887)

History of the town of Kirkland, New York by Gridley, A. D.
New York: Hurd and Houghton, 1874, 249 pgs.
p.149 - Manchester School stood on the cornor of Seneca Turnpike (Hwy-5) and Clinton Rd. This is the location of the home of John GREEN and Martha (Douglass) GREEN. In 2004 the Oneida Co Historical Society confirmed that the school was still standing and was now a day-care. The land for this school was deeded by John in 1838, 1/10 acre to Kirkland School District.

John married Martha Douglas between 1836 and 1837 in Oneida, NY. Martha (daughter of Isaac Douglas and Sarah Gleason) was born in 1798 in Westmoreland, Oneida, NY; died in 1845 in Kirkland, Oneida, NY; was buried in Barns Cemetery (Aka Kirkland Cem.), Kirkland (Westmoreland), Oneida, NY. [Group Sheet] [Family Chart]

Notes:

The 1820 and 1830 census birth dates for the wife of John GREEN do not match the birth date of Martha DOUGLASS (b.1800). I have suspected that John may have been married to someone prior to Martha. The "Barns Cemetery" records indicate that John was probably married 4 times. The dates in 1820 and 1830 match the birth date for Lucy ARNOLD (b.1788). I believe John married;
1st - Mary COOK (1791-1815) m.abt.1810
2nd - Lucy ARNOLD (1788-1836) m.abt 1816-1820 (mother of Mary GREEN)
3rd - Martha DOUGLASS (1800-1845) m.abt 1837-1838 (mother of Gardner D. GREEN)
4th - Eunice STOCKWELL (1795-1883) m.May 14, 1850

With the birth and death dates for Martha Douglass provided in the "Barns Cemetery" data from the OCHS, Martha is the daughter of Isaac and Sarah (GLEASON) DOUGLASS of Westmorland, Oneida, NY.
See LDS
Film Number: 170568, Page Number: 555, Reference number: 19275
Film Number: 170881, Page Number: 350, Reference number: 19145

In the 1880 Census, Mary Ann (GREEN) TARBOX lists her mother as born in MA but this was probably for Eunice STOCKWELL, her step-mother.

From: Mid-Atlantic Genealogies 1340-1940, A Collection of Family Records with Biographical Sketches Bearing the Name Douglas, New London Family 1575-1878. p.63
iii. MARTHA6, b. 1798; m. John Green, mechanic; d. Kirkland, 1845; left, Edward7 Green, Ilion, N. Y., and Gardner7 Green, Clinton, Mich.

Isaac married Sarah Gleason about 1793 in Westmoreland, Oneida, NY. Sarah was born between 1772 and 1777 in of New London, New London, CT; died in Oct 1827 in Clay, Onondaga County, New York. [Group Sheet] [Family Chart]

Notes:

mwd Joseph GLEZEN (father) 1810, 1810

The 1820 census lists a Mrs. DOUGLASS, living next to Daniel DOUGLASS in Whitestown. This would likely be Sarah since her husband died in 1811.

John married Esther Leach on 11 May 1746 in New London, Connecticut, USA. Esther was born in 1727 in New London, New London County, Connecticut; died on 6 Nov 1803 in New York. [Group Sheet] [Family Chart]