— born in Missouri, either Cooper Co., MO, or Clay Co., MO:
  5.  William K. THOMPSON, b. 1830/1; d. 1898, bur. Clay Co., MO
  6.  J. W. THOMPSON, b. 1832/3
  7.  Robert C. THOMPSON, Jr., b. 1834/5
  8.  Permelia C. THOMPSON, b. 1835/6
  9?  Clara Alice THOMPSON, b. 1837; d.s.p. 1837
10.  (Son B) THOMPSON, b. 1835-40
11.  (Son C) THOMPSON, b. 1835-40
12.  (Daughter B) THOMPSON, b. 1835-40

— born in Clay Co., MO:
13.  Ruth M. THOMPSON, b. 1841/2

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

Thompson, Robert C.

Roberts, Evaline

Mar 7, 1822

Todd Co.

2.  1830 Census Index/Images (online at Ancestry.com; Image #55 of 74; extracted by Diana Gale Matthiesen):

1830

MO

Cooper Co.

Roll M19_73

p. 221

Ln. 10

Robert Y Thompson

110 010 - 200 010

011000-010000

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	4 or under	1825-1830	= Son A
1 white male	5-9	1820-1825	= Gideon (b. 1823)
1 white male	20-29	1800-1810	= Robert (b. 1801)
2 white females	4 or under	1825-1830	= Virginia (b. 1829/30) = Daughter A
1 white female	20-29	1800-1810	= Evaline (b. 1801)
1 male slave	10-23	1806-1820	= ?
1 male slave	24-35	1794-1806	= ?
1 female slave	10-23	1806-1820	= ?

I have no explanation for why Robert's middle initial is "Y," but it clearly is.  Other THOMPSONs in county:  Robert's brothers, Gideon R. THOMPSON and John THOMPSON.

3.  1840 Census Index/Images (online at Ancestry.com, Image #13 of 70; extracted by Diana Gale Matthiesen):

1840

MO

Clay Co.

Roll M704_222

pp. 7A-7B

Ln. 25

Robert C Thompson

221 111 - 202 001

111000-130000

0400000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 white males	4 or under	1835-1840	= Son C = Son B
2 white males	5-9	1830-1835	= J. W. (b. 1832/3) = William (b. 1830/1)
1 white male	10-14	1825-1830	= Son A
1 white male	15-19	1820-1825	= Gideon (b. 1823)
1 white male	20-29	1810-1820	= ?
1 white male	30-39	1800-1810	= Robert (b. 1801)
2 white females	4 or under	1835-1840	= Daughter B = Permelia (b. 1835/6)
2 white females	10-14	1825-1830	= Virginia (b. 1829/30) = Daughter A
1 white female	30-39	1800-1810	= Evaline (b. 1801)
1 male slave	9 or under	1830-1840	= ?
1 male slave	10-23	1816-1830	= ?
1 male slave	24-35	1804-1816	= ?
1 female slave	9 or under	1830-1840	= ?
3 female slaves	10-23	1816-1830	= ? ? ?
4	persons employed in agriculture

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com; Image #13 of 97):  Liberty Twp., Clay Co., MO, Roll M432_396, p. 306A, 79/79, enumerated 15 Aug 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Thompson R C	50	M		Farmer	4000	Ky
"    Eveline	50	F				do
"    Virginia	20	F				do
"    Wm K	19	M		Farmer		Mo
"    J W	17	M		do		do
"    Robt C Jr	15	M		do		do
"    Permelia C	14	F				do
"    Ruth M	8	F				do

5.  1860

6.  1870

7.  1880

8.  1890

10.  Elizabeth Prather Ellsberry.  1962.  Clay County, Missouri, Cemetery Records.  2 vols.  Self-published, Chillicothe, MO (online at Ancestry.com):

Name	Birth	Death	Age
Robert Thompson	1801	1857
Eveline Thompson	1801	1893
William Thompson	[1830/1]	1898	67 yrs
Clara Alice Thompson	1837	1837

Clara appears to be their daughter because the only other THOMPSONs in this index are Robert & Eveline's son, Gideon, and his wife, Nancy, plus a James (b. 1854) who appears to be Gideon & Nancy's son.  As this database is merely an indes, there may be more information in Ellsberry's book and/or on the tombstones.

11a.   Stuart Seely Sprague.  1984.  Kentuckians in Missouri.  Genealogical Publ. Co., Baltimore, MD. On p. 154, cites next source.

11b.  Anon.  1885.  History of Clay and Platte Counties, Missouri.  National Historical Co., St. Louis, p. 881.  Biographical sketch of son, Col. Gideon W. THOMPSON. [not seen]