Secondary sources are assuming that Zachariah's surname derived, like CATRON, from KETTENRING.  I'm not certain this is a valid assumption.

— born in Jefferson Twp., Owen Co., IN:
6.  Lewis / Louis COTTON, b. 1835/6
7.  Zachariah COTTON, b. 1836/7 or 19 Jan 1835; d. 20 Dec 1902
8.  Andrew COTTON, b. 14 May 1838; d. 15 Feb 1903, Sullivan Co., MO
9.  Mary Jane COTTON, b. 1839/40

1.  Marriage Record:

2.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Zachariah COTTON Birth: About 1799, North Carolina Marriage: About 1825, Russell, Virginia Spouse: Mary A. STROUP Birth: About 1797, Russell, Virginia; Death: About 1855, Vandalia, Owen, Indiana Child-1: Jesse Ray COTTON; Birth: About 1827, Russell, Virginia Child-2: John COTTON; Birth: About 1831, Russell, Virginia Source: patron submission

3.  1830 Census Index/Images (online at Ancestry.com, Image #13 of 78 — list was roughly alphabetized; extracted by Diana Gale Matthiesen):¤•

1830

VA

Russell Co.

Roll 199

p. 143

Ln. 19

Cotton Zachariah

100 010 - 120 001

no slaves

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1825-1830	= Jesse (b. 1827)
1 male	20-29	1800-1810	= Zachariah (b. 1801)
1 female	4 or under	1825-1830	= Daughter C
2 females	5-9	1820-1825	= Daughter B = Daughter A
1 female	30-39	1790-1800	= Mary (b. 1796/7)

4.  1840 Census Index/Images (online at Ancestry.com, Image #3-4 of 8; extracted by Diana Gale Matthiesen):¤•

1840

IN

Owen Co.

Jefferson Twp.

Roll 89

pp. 109B-110A/212-213

Ln. 25

Zachariah Cotton

221 001 - 101 100 100

0200000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	4 or under	1835-1840	= Andrew (b. 1837/8) = Zachariah (b. 1836/7)
2 males	5-9	1830-1835	= Louis (b. 1835/6) = John (b. 1831)
1 male	10-14	1825-1830	= Jesse (b. 1827)
1 male	30-39	1800-1810	= Zachariah (b. 1801)
1 female	4 or under	1835-1840	= Mary Jane (b. 1839/40)
1 female	10-14	1825-1830	= Daughter C
1 female	15-19	1820-1825	= Daughter A or B
1 female	40-49	1790-1800	= Mary (b. 1796/7)
2	persons employed in agriculture

5.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #22 of 29):  Jefferson District, Owen Co., IN, Roll M432_164, p. 129B, 626/626, enumerated 21 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

1850:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	11
626	626	Zachariah Cotton	50	M	W	Farmer	1000	North Carolina	1	4
		Mary A	53	F	W			Virginia
		Louis	14	M	W			Indiana
		Zachariah	13	M	W			Do
		Andrew	12	M	W			Do
		Mary J	10	F	W			Do

How can only Zachariah have been "married within the year" (Column 10), especially when his wife wasn't?  This enumerator also mis-used Column 11 (i.e., it should have been blank for our subject with, instead, a tick mark for each of his four children).  On both counts, we have to figure the enumerator either hadn't been instructed adequately or hadn't listed to his instructions.

6.  Sally's Family Place — Mulberry Grove (www.sallysfamilyplace.com). 

7.  Messages posted to the Cotton Family Genealogy Forum (online at GenForum.com).

8.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).