It's difficult to fit the daughters below into the scenario above.  I do not know the source of the birthdates for Elizabeth and Nancy, but Henrietta's birthdate is from the 1850 Census; however, like most middle-aged women, Henrietta was probably lying about her age (one source says she was born 1807).  What we do know is that we have six daughters above and only five named below.

.  Elizabeth COWDEN, b. 1806; m. William NEAL, s/o Thomas Edward NEAL & Jane McCAMMON 
.  Nancy COWDEN, b. 1808; m. Mr. FREDRICK 
.  Henrietta A. COWDEN, b. 1808/9, KY 
.  Martha Ann COWDEN, m. Mr. POSEY 
.  Eleanor "Ellen" COWDEN

A.  Subject is said to use names John and William interchangeably.

B.  I've never dealt with anyone who managed to elude so many census takers!  Does anyone know where he was in 1830, 1840, 1850, and 1860?

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

Cowden, John

Tremble, Mary

17 Dec 1802

Fayette Co.

2.  Jordan R. Dodd, ed.  1993.  Indiana Marriages: Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-228):

Cowden, John

Richey, Rebecca

12 Nov 1815

Knox Co.

3.  Census Index:  U.S. Selected Counties, 1810 (Broderbund CD-313):
John/William Cowden not found.

4.  Family Quest Archives:  Indiana Federal Census 1820:  Fayette, Ripley, Spencer, Sullivan, Warwick, and Wayne Counties.  Heritage Quest CD M33-15 (extracted by Diana Gale Matthiesen):

1820

IN

Sullivan Co.

p. 126

John Cowden

100010-32110

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1810-1820	= John (b. ca. 1816)
1 male	26-44	1775-1794	= John (b. 1778)
3 females	9 or under	1810-1820	= Daughter F = Daughter E = Daughter D
2 females	10-15	1804-1810	= Daughter C = Daughter B
1 female	16-25	1794-1804	= Daughter A
1 female	26-44	1775-1794	= Rebecca

Four lines down from James TRIMBLE and three lines down form Theodosha (SMITH) BOOKER. 

5.  Family Quest Archives:  Indiana Federal Census 1830:  Fayette, Lawrence, Gibson, Sullivan, Boone, Vermillion, Hamilton, Rush, Martin, Madison, Allen, Pike, Decatur, St. Joseph, and Elkhart Counties.  Heritage Quest CD M19-26 (extracted by Diana Gale Matthiesen):

1830

IN

Sullivan Co.

p. 174

John Couhorn?

110 001 - 211 001

These data indicate a man in his 30s.  He is not our subject, who should be in his 50s in 1830.

6.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):
John/William Cowden not found.

7.  Census Microfilm Records:  Indiana, 1850 (Broderbund CD-302):
John/William Cowden not found.

8.  Census Records:  Indiana, 1860 (Broderbund CD-304):
John/William Cowden not found (none in Indiana old enough to be our subject).

9.  1906 Letter from Eliza Trimble to Winifred Markee Miles.  Contributed by Janet May.

10.  Archives of the TRIMBLE-L mailing list (online at RootsWeb.com):  a post from Janet May give's "William's" birthdate as 1778, place unknown, and deathdate as 15 Sep 1863, Sullivan Co., IN.   A post by Allen Griffith also gives John's birth/death years as "1778-1863."

11.  A gedcom file online at GENDEX. [link died]