Secondary sources have John b. 1788 or 1794, but two censuses have him born 1800-1810 and one census between 1794 and 1801.  Given his marriage date and his wife's birthdate, it had to be between 1800 and 1802.

— born in KY, possibly in Christian, Trigg, or Ballard Co.:
11.  Lycurgus RASCO, b. 1841/2
12.  Solon RASCO, b. 27 Sep 1844
13.  Mary Lee RASCO, b. 1846; d. 1846-50

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

Rasco, John

Taylor, Lucy

20 Jul 1820

Christian Co.

No marriage records found for Margaret or Catherine, who would have been expected to marry by 1850.

1b.  Marriage Index:  Kentucky, 1851-1900.  Liahona Research, Orem, UT (Broderbund CD-233):  there are RASCO/RASCOE marriages in Ballard, Christian, Caldwell, Hopkins, Lyon and Caldwell Cos., who are no doubt kin of our subjects, but none appear to be our subjects' children.

2a.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):  not found as head-of-household, but the newlyweds appear to be living with John's widowed mother, Rachel RASCO.

2b.  1820 Census Index and Digital Images (online at Ancestry.com; Image #15 of 23; extracted by Diana Gale Matthiesen):

1820

KY

Christian Co.

p. 43

Rachel Rasco

000100-00101

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	19-25*	1794-1801	= John (b. 1800/1)
1 white female	16-25	1794-1804	= Lucy (b. 1802)
1 white female	45 or over	in or bef. 1775	= Rachel
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25; therefore, any individual in column three is duplicated in column four.  By subtracting the number in column three from the number in column four, you can create an age class "19-25."

Listed 12 lines down from Jesse FORT, who is next door to Garey FORT, who is next door to Micajah FORT.

3.  1830 Census Index and Digital Images (online at Ancestry.com; Image #89 of 94; extracted by Diana Gale Matthiesen):

1830

KY

Christian Co.

p. 51

John Rasco

110 020 - 220 010

220 000-011 000

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	4 or under	1825-1830	= Joshua (b. 1825)
1 white male	5-9	1820-1825	= William (b. 1821)
2 white males	20-29	1800-1810	= ? = John (b. 1800-02)
2 white females	4 or under	1825-1830	= Daughter A = Catherine (b. 1827)
2 white females	5-9	1820-1825	= Margaret (b. 1824) = Cassandra (b. 1822)
1 white female	20-29	1800-1810	= Lucy (b. 1802)
2 male slaves	9 or under	1820-1830	= names unknown
2 male slaves	10-23	1806-1820	= names unknown
1 female slave	10-23	1806-1820	= name unknown
1 female slave	24-35	1794-11806	= name unknown

Living next door to James FORT, who is living next door to Joshua TAYLOR, who is living two doors down from Micajah FORT.  He is the only RASCO/&c. in KY on this CD.

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

1840

Roseo, John

KY

Christian Co.

p. 196

He is the only RASCO/&c. in Christian Co. on this CD.

4b.  Christian County Genealogical Society (Hopkinsville, KY).  1995.  Christian County, KY, Census Records, 1820-1830-1840.  Simmons Historical Publ., Melber, KY.  On p. 62 (of the book, not the census):

1840

Rosco

John

102 201 000 - 211 101 000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= Jack (b. 1837/8/9)
2 males	10-14	1825-1830	= ? = Joshua (b. 1825)
2 males	15-19	1820-1825	= William (b. 1821) = ?
1 male	30-39	1800-1810	= John
2 females	4 or under	1835-1840	= Nancy (b. 1839/40) = Lucy (b. 1835/6)
1 female	5-9	1830-1835	= Alvira (b. 1833/4)
1 female	10-14	1825-1830	= Catherine
1 female	15-19	1820-1825	= Margaret
1 female	30-39	1800-1810	= Lucy (b. 1801/2)

The unnamed males above were not in the 1830 census, so cannot be our subject's children.  They are living next door to their son-in-law, David Fort DAVIS. 

5.  1850 Census Index/Microfilm (online at GenealogyLibrary.com; mis-indexed as "Rasen"):  Ballard Co., KY, p. 300A, 707/707, enumerated 10 Sep 1850 (extracted by Diana Gale Matthiesen):

Lucy Rasco	48	F		200	Va
Alvira  "	16	F			Ky
Lucy    "	14	F			Ky
Jack    "	11	M			Ky
Nancy   "	10	F			Ky
Lycurgus "	8	M			Ky
Solon   "	6	M			Ky

Living next door to her son, William A. RASCO.

6.  1860

7.  1870

8.  1880

9.  WorldConnect (online at RootsWeb.com).

10.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs online at FamilySearch.org).

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