— born in GA:
3.  Mary A. ALEXANDER, b. 1824/5
4.  Sarah E. ALEXANDER, b. 1827/8
5.  Louisa C. ALEXANDER, b. 1831/2
6.  Thomas J. ALEXANDER, b. 1836/7

1a.  LDS.  Family Search: Internet Genealogy Service: IGI - International Genealogical Index (online at FamilySearch.org).

Joseph Young ALEXANDER Birth: 10 Dec 1792, Georgia; Death: 30 Mar 1857, Newman, Coweta, Georgia Marriage: 07 Sep 1820, Newman, Coweta, Georgia Spouse: Ann McAUSLIN Birth: Jul 1797, Georgia; Death: Newman, Coweta Georgia Source: patron submission

Joseph Y. ALEXANDER Spouse: Elizabeth H. CORBIN Marriage: 17 Oct 1848, Coweta, Georgia Source: Record of Marriages, 1827-1966. Georgia. Court of Ordinary (Coweta County)

1b.  Jordan R. Dodd, ed.  1993.  Georgia Marriages: Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-226):

Alexander, Joseph Y

Corbin, Elizabeth H

10/17/1848

Coweta Co.

2.  1820 Census Index/Images (online at Ancestry.com):  the only Joseph ALEXANDER in Georgia is too old (45+) to be our subject.  There's no Joseph ALEXANDER in South Carolina.

3.  1830 Census Index/Images (online at Ancestry.com, Image #3-4 of 8; extracted by Diana Gale Matthiesen):

1830

GA

Oglethorpe Co.

Capt. Dacking's Dist.

Roll 20

p. 98

Ln. 7

Joseph Y Alexander

120 101 - 210 010

100010-100200

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	4 or under	1825-1830	= Son
2 white males	5-9	1820-1825	= John R. (b. 1822/3) = A. W. (b. 1821/2)
1 white male	15-19	1810-1815	= Son? Boarder?
1 white male	30-39	1790-1800	= Joseph (b. 1792)
2 white females	4 or under	1825-1830	= Sarah E. (b. 1827/8) = Daughter
1 white female	5-9	1820-1825	= Mary (b. 1824/5)
1 white female	20-29	1800-1810	= Anna (b. 1797)
1 male slave	9 or under	1820-1830	= ?
1 male slave	55-99	1730-1775	= ?
1 female slave	9 or under	1820-1830	= ?
2 female slaves	36-54	1775-1794	= ? ?

Given Joseph's age, the teenage boy could be his son from a prior marriage.  Either the enumerator erred or Anna is fibbing about her age.

4.  1840 Census Index/Images (online at Ancestry.com, Image #3-4 of 8; extracted by Diana Gale Matthiesen):

1840

GA

Coweta Co.

Roll 39

pp. 319A-319B

Ln. 19

Joseph Y Allexander

200 200 100 - 022 100 100

000000-110100

0100001

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 white males	4 or under	1835-1840	= Thomas J. (b. 1836/7) = Son
2 white males	15-19	1820-1825	= John R. (b. 1822/3) = A. W. (b. 1821/2)
1 white male	40-49	1790-1800	= Joseph (b. 1792)
2 white females	5-9	1830-1835	= Louisa C. (b. 1831/2)
2 white females	10-14	1825-1830	= Sarah E. (b. 1827/8) = Daughter
1 white female	15-19	1820-1825	= Mary A. (b. 1824/5)
1 white female	40-49	1790-1800	= Anna (b. 1797)
1 female slave	9 or under	1830-1840	= ?
1 female slave	10-23	1816-1830	= ?
1 female slave	36-54	1785-1804	= ?
1	persons employed in agriculture
1	persons employed in learned professions and engineering

5.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #112-113 of 196):  19th Division, Coweta Co., GA, Roll M432_66, pp. 338B-339A, 782/782, enumerated 4 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Jos Y Alexander	57	M		Pres Clergyman	2000	NC
Elizabeth H	32	F				SC
[next page]
A W Alexander	28	M		Clerk		SC
John R	27	M		ass P M		"
Mary A	25	F		Teacher		Ga
Sarah E	22	F				"
Louisa C	18	F				"
Thos J	13	M				"
Emar	9/12	F				"

All the children appear to be Joseph's, so where are Elizabeth's children from her marriage with Lyman CORBIN?

6.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 13):  Hogansville P.O., Hogansville, 700th Dist., Troup Co., GA, Roll M653_138, p. 252, PN 78, 539/499, enumerated 1 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Jas M Boyd	78	M		Farmer	3000	5000	SC
Mary   "	68	F					"
E Alexander	43	F					"
Wm Boyd	33	M		"			"
Emma Alexander	10	F					Ga
Jno H Cooper	27	M		"	1000		"