1.  Marriage Record:  my understanding is that the Sullivan County marriage books were lost when the Sullivan County Courthouse burned down in 1853; and, certainly, I have found no source of pre-1853 Sullivan County marriages.  But a file at WorldConnect cites "Sullivan Co., Indiana, Marriages, Book 1, Page 52" as the source for the marriage of Joseph TRIMBLE and Catherine CARRICO on 28 Jan 1823.  It may be that some fragmentary records survived, as is often the case in a fire.

2.  1830 Census Index/Images (online at Ancestry.com, Image #35 of 76 — indexed "Tmble"; extracted by Diana Gale Matthiesen):¤•

1830

IN

Sullivan Co.

Roll 26

p. 174

Ln. 2

Joseph Trimble

110 001 - 210 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1825-1830	= James (b. 1825)
1 male	5-9	1820-1825	= Charles G. (b. 1823)
1 male	30-39	1790-1800	= Joseph (b. 1794/5/6)
2 females	4 or under	1825-1830	= Mary (b. 1829) = Martha (b. 1828)
1 female	5-9	1820-1825	= Sarah (b. 1824)
1 female	20-29	1800-1810	= Catherine (b. 1801)

Listed next to John COWHORN (æ 30-40).

3.  1840 Census Index/Images (online at Ancestry.com, Image #21-22 of 90; extracted by Diana Gale Matthiesen):¤•

1840

IN

Sullivan Co.

Roll 94

pp. 59B-60A

Ln. 3

Joseph Trimble

101 100 100 - 112 101

0300000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= Josiah (b. 1835)
1 male	10-14	1825-1830	= James (b. 1825)
1 male	15-19	1820-1825	= Charles (b. 1823)
1 male	40-49	1790-1800	= Joseph (b. 1794/5/6)
1 female	4 or under	1835-1840	= Catharine (b. 1839)
1 female	5-9	1830-1835	= Margaret (b. 1831)
2 females	10-14	1825-1830	= Mary (b. 1829) = Martha (b. 1828)
1 female	15-19	1820-1825	= Sarah (b. 1824)
1 female	30-39	1800-1810	= Catherine (b. 1801)

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #32 of 72):  District No. 105, Haddon Twp., Sullivan Co., IN, Roll M432_173, pp. 213B-214A, 204/206, enumerated 15 Aug 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Mathiesen):¤•

Joseph Trimble	55	M		Farmer	2000	Ky
Catherine Trimble	49	F				Ind'a
Charles Trimble	26	M				Ind'a
Mary	21	F				Ind'a
Margaret	19	F				Ind'a
Josiah	14	M				Ind'a
Catharine	11	F				Ind'a
William M	6	M				Ind'a
Harriet	3	M				Ind'a

Listed two households from Catherine's brother, Reason CARRICO. 

5.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #35 of 51):  Carlisle P.O., Haddon Twp., Sullivan Co., IN, Roll M653_298, p. 741, PN 35, 244/244, enumerated 16 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Joseph Trimble	64	M		farmer	2500	750	Ky
Catherine  "	60	F					Ind
Catherine  "	22	F					do
Wm         "	16	M					do
Ha???tt   "	13	M					do

6.  1870 Census Every-Name-Index/Images (online at Ancestry.com; Image #46 of 57):  Merom P.O., Hadden Twp., Sullivan Co., IN, Roll 361, p. 115B, PN 46, enumerated 23 Jul 1870, 343/323, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Trimble Joseph	74	M	W	Retired Farmer	Kentucky
_______ Catharine	70	F	W	Keeping house	Indiana

Listed next to their son, William Murphy TRIMBLE, on one side; and, on the other side, listed next to George BOOKER, who is next to Theophilos BOOKER, who is next to their daughter, Sarah Elizabeth (TRIMBLE) WILLIS, and her husband John Robards WILLIS. 

7.  Find-a-Grave: Entries (online at findagrave.com):

Name	Joseph Trimble	Catherine Carrico Trimble
Birth	Feb. 3, 1796 Lexington, Fayette Co., KY	Jan. 15, 1801 Lexington, Fayette Co., KY
Death	Jan. 12 1873 Sullivan Co., IN	Jan. 31, 1871 IN
Burial	Trimble Cemetery, Sullivan County, Indiana
Inscription	JOSEPH TRIMBLE DIED JAN. 12, 1873 AGED 77 YS CATHARINE HIS WIFE DIED JAN. 3, 1871 AGED 71 YS
Memorial #	33707860	33708071

8.  Bureau of Land Management, Eastern States, General Land Office. Official Land Patent Records Site:

Joseph Trimble received these land patents in Sullivan Co., IN
1829 Jul 02	W½	SW¼	S5.T6N.R8W	80 acres
1831 Dec 31	E½	SW¼	S5.T6N.R8W	80 acres
1839 Feb 01	SW¼	SE¼	S5.T6N.R8W	40 acres
1839 Aug 01	NE¼	SE¼	S5.T6N.R8W	40 acres

There was a Charles Trimble and a William Trimble acquiring adjacent patents in the same Section at about the same time as Joseph.

9.  John B. Hayword.  ca. 1845.  Family Record for J. & K. Trimble (photostat kindly provided by Georgia Pirtle; transcription by Diana Gale Matthiesen):

Family Record for J. & K. Trimble by John B. Hayward Joseph Trimble Son of James & Sarah Trimble Born February 3rd 1796 &  Katherine Daughter of Charles & Martha Carica Born Jan 15th 1801 And Married to Joseph Trimble Jan 28th 1823 Charles G Trimble Born Nov 26th 1823 Sarah Trimble Born November 23rd 1824 James Trimble Born December 17th 1825 Martha Trimble Born June 16th 1828 Mary Trimble Born Novr 15th 1829 Margaret Trimble Born May 13th 1831 Eliza Trimble Died August 2nd 1834 aged 10 m. [unreadable] Josiah Carica Trimble Born August 8th 1835 Katherine Trimble Born October 21st 1839 William M. Trimble Born Sep 4 1844...

Harriet Trimble Born Decr [torn off]

The page goes on with some "Wisdoms" in small text that I can't deciper in the photostat, but which doesn't appear to have genealogical significance. Harriet's name appears to have been added later, in the space to the right of the other children's names, which suggests the "Record" was written after the birth of William, in Sep 1844, but before the birth of Harriet, in Dec of 1846.

10.  There is said to be a Trimble Bible in the possession of Mrs. Tessie James Miller (536 South Hope Street, Biola Hotel, Box 325, Los Angeles, CA 90017), at least, as of 13 Sep 1973.

11.  Broderbund.  World Family Trees.  Vol. 19, Pedigree No. 1592, submitted by Charles Toca.

12.  LDS.  Family Search: Internet Genealogy Service:  AF - Ancestral File (online at FamilySearch.org).

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