Our subject's parents may be this couple:
Father:  Thomas William WYATT
Mother:  Mary NEEDHAM
but the connection is not proven.

Secondary sources give William and Rachel two additional children:
.  Catherine WYATT
.  Sophia WYATT
but see the sources below for reasons these two cannot be their daughters.

1.  Family Group Sheet by Betty Ann (Matthiesen) Cogliati and her grandmother, Maude Irene (Thompson) Rose.

2a.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):

Wyatt, William

Thompson, Rachel

19 Jan 1825

Todd Co.

2b.  Jordan Dodd, ed.  1998.  Marriage Index:  Missouri, 1851-1900  (Broderbund CD-234):

Wyett, William

???, Jeanette A.S.

11 Jul 1869

Grundy Co.

3a.  Census Index:  U.S. Selected Counties, 1830 (Broderbund CD-315):

1830

Wyatt, William

MO

Franklin Co.

Boeff Twp.

p. 140

He's the only William WYATT in Missouri, at least in this index, but he is not our subject (see next source).

3b.  Family Quest Archives:  Missouri Federal Census 1830:  Lincoln, Marion, Chariton, Washington, Jefferson, Franklin, Gasconade, Crawford, Cole, Montgomery, Pike, St. Charles, St. Louis, St. Genevieve, Perry, St. Francois, and Cape Girardeau Counties.  Heritage Quest CD M19-72 (extracted by Diana Gale Matthiesen):

1830

MO

Franklin Co.

p. 140A

William Wyatt

001 010 100 - 221 110

These data indicate that this William was born 1780-90, so he could not be our subject.  Even if this were our subject's father, also named William, and even though the next younger male (b. 1800-1810) could be our William, there is no son in the house under age five, so again, this is not our subject.

4a.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):

1840

Wiatt, William

MO

Livingston Co.

Jackson Twp.

p. 274

The indexer mis-read the township (see next source).

4b.  Family Quest Archives:  Missouri Federal Census 1840:  Lewis, Lincoln, Linn, and Livingston Counties.  Heritage Quest CD M704-225 (extracted by Diana Gale Matthiesen):

1840

MO

Livingston Co.

Franklin Twp.

p. 275A

William Wiatt

121 001 - 010 001

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= Benjamin Franklin (b. 1838)
2 males	5-9	1830-1835	= Thomas Jackson (b. 1835) = James N.B. (b. 1831)
1 male	10-14	1825-1830	= John (b. 1828)
1 male	30-39	1800-1810	= William (b. 1802/3)
1 female	5-9	1830-1835	= Mary (b. 1833)
1 female	30-39	1800-1810	= Rachel (b. 1803)

There is no room here for Catherine, even if she was born in 1829 and not 1823.

5.  Grundy County, MO, 1850 Census (online at the Grundy County MOGenWeb site):  Dist. #35, p. 410, enumerated 15 Aug 1850, 341/342.

Wyatt Wm.	47	M	Farmer	1000	Tenn
Wyatt Rachel	47	F			Ky
Wyatt James N.B.	19	M	Farmer		Mo
Wyatt Jackson	15	M	Farmer		Mo
Wyatt Franklin	13	M			Mo
Wyatt Boon	8	M			Mo

Catharine did not marry until 1858, so if she was their daughter, she should be here at home.

6.  1860 Census Images (online at Ancestry.com; Image #3 of 16):  Middlebury P.O., Franklin Twp., Grundy Co., MO, p. 461, PN 169, 1353/1196, enumerated 11 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Wm Wyatt	57	M		Farmer	2000	1000	Tenn
Rachal	56	F					Ky
Andrew	14	M					Mo

Andrew was not in the household in 1850.  Is he really their son?  Where is Boone?  Are Boone and Andrew the same person?  Boone died in the Civil War, so he was alive in 1860.  Listed five households from son, John Thompson WYATT. 

7.  Mrs. B.F. Hoover & Mrs. O.L. Livingston.  1964. Wyatt Cemetery, Grundy Co., MO (online at the Grundy County MOGenWeb site):

WYATT	Rachel		Jul 20, 1870	65y-3d; w/o Wm.
WYATT	Jeanetta A.	Oct 8, 1831	Dec 23, 1870
WYATT	William		Jul  9, 1880	h/o Rachel

Rachel died in 1868, not 1870.

8.  Mrs. Lee Hathaway & Mrs. Vernal Ralston.  1962-64. Spickard Masonic Cemetery, Grundy County, MO (online at the Grundy County MOGenWeb site):

WRIGHT	Wife of W.D.		21 Aug 1918	(Jeanette A. Roundsville?)
WYATT	William David	8 Dec 1870	12 Feb 1964	Son of William T. & Jeanette A. (Roundsville)

What made them think Mrs. W.D. WRIGHT was Jeanette A. "ROUNDSVILLE"?  (Of course, it's ROUNSAVELL, not ROUNDSVILLE.)

9.  LDS.  Family Search: Internet Genealogy Service: Ancestral File.

The AF has Sophia WYATT as a daughter of William and Rachel.  She is not.  She is the daughter of John WYATT & Mary Ann DISBURY.  I suspect John may be a brother to our subject because John's widow moved to Grundy [now Mercer] Co. after John's death.  (Spickard is in northern Grundy Co., almost on the Mercer Co. line, and kinfolk  lived on both sides of the county line.) Thank you to Diane Schroeder for bringing this error to my attention.

The AF has Catherine WYATT (b. 1829) as a daughter of William & Rachel.  I don't see how she can be.  No daughter of that age shows up in the 1840 or 1850 census, nor does a daughter named Catherine, of any age, show up in 1850.  Catharine E. WYATT married Jason B. ST. CLAIR in Grundy Co., MO, in 1858, so she should have been in her parents' household in both 1840 and 1850.  She is not in William & Rachel's.

10.  Emails from Diane Schroeder.

11.  Emails from Joleen Axtell.