Given the age difference between Eliakim and Lodama, one would immediately suspect Eliakim had a prior wife.  A prior wife would allow for some additional children born before 1805.

— born in Otsego, Otsego Co., NY; baptized 17 Aug 1817, Congregational Church, Exeter, Otsego Co., NY:
2.  Horace CORBIN, b. 10/19 Dec 1806
3.  Abel Rathbone CORBIN, b. 24 May 1808
4.  Lavinia / Lavina CORBIN, b. 7 Jul 1810
5.  Eli Lyon CORBIN, b. 7 Feb 1812

— born in Exeter, Otsego Co., NY:
6.  Lucia Amanda CORBIN, b. 31 Dec 1821

Harvey is said to be son of our subject; however, his birthdate cannot be close to his baptismal data because it would be too close to the birth of Horace.  Harvey is 45 in the 1850 census, suggesting he was born in either 1804 or 1805.  Was he a twin of Arian?  Horace cannot have been born in 1807, because then his birthdate would be too close to Abel's.  Is Harvey really their son?  There is room for him in the 1810 census.

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

Eli CORBIN, Abel Rathbun CORBIN, Horace CORBIN, Levina CORBIN Christening: 17 Aug 1817, Congregational Church, Exeter, Otsego, New York Father: Eliakam L. CORBIN; Mother: Lodamia Source: Church Records, 1806-1861, Congregational Church (Exeter, New York)

The fact that the children were baptized together in 1817 suggests the family moved from Otsego to Exeter in 1817 (and joined a new church).

2.  1810 Census Index/Images (online at Ancestry.com, Image #1 of 8; extracted by Diana Gale Matthiesen):¤•

1810

NY

Otsego Co.

Otsego

Roll 34

p. 203

Ln. 4

E. Corbin

30010-21100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
3 males	9 or under	1800-1810	= Abel (b. 1808) = Horace (b. 1806) = Harvey? (b. 1804/5)
1 male	26-44	1765-1784	= Eliakim (b. 1777)
2 females	9 or under	1800-1810	= Lavinia (b. 1810) = Arian (b. 1805)
1 female	10-15	1794-1800	= ?
1 female	16-25	1784-1794	= Lodama (b. 1784)

3.  1820 Census Index/Images (online at Ancestry.com, Image #5 of 5; extracted by Diana Gale Matthiesen):¤•

1820

NY

Otsego Co.

Exeter

Roll M33_74

p. 171

Ln. 6

Eliakim Corbin

130010-02010-0-400

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1810-1820	= Eli (b. 1812)
3 males	10-15	1804-1810	= Abel (b. 1808) = Horace (b. 1806) = Harvey? (b. 1804/5)
1 male	26-44	1775-1794	= Eliakim (b. 1777)
2 females	10-15	1804-1810	= Lavinia (b. 1810) = Arian (b. 1805)
1 female	26-44	1775-1794	= Lodama (b. 1784)
4	persons engaged in agriculture

4.  1830 Census Index/Images (online at Ancestry.com, Image #7 of 16 — indexed "Eickim L Crtin"; extracted by Diana Gale Matthiesen):¤•

1830

NY

Chenango Co.

McDonough

Roll 86

p. 97

Ln. 10

Eliakim L Corbin

000 110 010 - 010 110 100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	15-19	1810-1815	= Eli (b. 1812)
1 male	20-29	1800-1810	= ?
1 male	50-59	1770-1780	= Eliakim (b. 1777)
1 female	5-9	1820-1825	= Lucia (b. 1821)
1 female	15-19	1810-1815	= Lavinia (b. 1810)
1 female	20-29	1800-1810	= Arian (b. 1805)
1 female	40-49	1780-1790	= Lodama (b. 1784)

None of the three born before 1810 is yet married, so it's hard to say who's still at home and who's working out or off to school or whatever.

5.  1840 Census Index/Images (online at Ancestry.com, Image #13-14 of 16; extracted by Diana Gale Matthiesen):¤•

1840

NY

Chenango Co.

McDonough

Roll 273

pp. 118A-118B

Ln. 14

Eliakim L Corbin

001 020 001 - 010 110 010

0300000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-14	1825-1830	= ?
2 males	20-29	1810-1820	= ? = Eli (b. 1812)
1 male	60-69	1770-1780	= Eliakim (b. 1777)
1 female	5-9	1830-1835	= grandchild?
1 female	15-19	1820-1825	= Lucia (b. 1821)
1 female	20-29	1810-1820	= ?
1 female	50-59	1780-1790	= Lodama (b. 1784)
3	persons employed in agriculture

It's hard to say who's in the household at this point. 

6.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  can't find Lodama — or George & Amanda (CORBIN) HOWELL.

7.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #559 of 560):  City of Washington P.O., Washington City (Ward 5 — mis-indexed as being in Ward 4), District of Columbia, Roll M653_103, p. 560, PN 156, 1196/1120, enumerated 1 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

George P Howell	43	M		Clerk in Depart.	$10,000	$1,000	Pennsylvania
Amanda    Do	41	F					New York
Louisa Corbin	75	F					Connecticut
Frank    Do	13	M					New York
Mary Wincoses?	21	F					Do
Lavenia Hamlin	15	F				$1,000	Pennsylvania

Louisa has to be Amanda's mother, Lodamia (RATHBONE) CORBIN.  Frank CORBIN appears to be son of Amanda's brother, Eli Lyon CORBIN.  Lavenia HAMLIN appears to be the orphaned daughter of Amanda's sister, Lavinia (CORBIN) HAMLIN.  I don't know who Mary is.

8.  Harvey M. Lawson, compiler.  1905.  Descendants of Clement Corbin of Muddy River (Brookline, Ma. and Woodstock, Ct): with notices of other lines of Corbins.  Hartford Press, Hartford, CT (online at Ancestry.com and at GoogleBooks):

p. 93

FIFTH GENERATION... 112.  ELIAKIM LYON CORBIN (Peleg, Samuel, James, Clement), b. Oct. 7, 1777, at Woodstock, Conn.; m. Lodama Rathbone Jan. 6, 1805.  She was the dau. of Abel and Anna (Gales) Rathbone, formerly of Nova Scotia.  They had nine children; Lodama, the sixth, was b. Sept. 2, 1784.  He removed soon after marriage from Woodstock to Exeter, Otsego County, N. Y., and, in 1822 to McDonough, Chenango County, N. Y. where he died May 10, 1841, and she d. in 1864. Children:   259.   i.   ARIAN, b. Nov. 3, 1805.   260.   ii.   HORACE, b. Dec. 19, 1806.   261.   iii.   ABEL RATHBONE, b. May 24, 1808.   262.   iv.   LAVINIA, b. July 7, 1810.   263.   v.   ELI LYON, b. Feb. 7, 1812; m. Abigail B. Taintor.       vi.   LUCIA AMANDA, b. Dec. 31, 1821; m. George P. Howell, Sept. 15, 1847.  They resided at Washington and Jersey City, he was in the real estate business; no ch.; she d. Jan. 31, 1878; he d. Nov. 1891. ...

9.  James H. Smith.  1880.  History of Chenango and Madison Counties, New York.  D. Mason & Co., Syracuse, NY (online at Ancestry.com):

p. 377

The First Presbyterian Church of McDonough was organized July 28, 1814, by Rev. John Truair of Sherburne, with fourteen members, who were mostly from Massachusetts, and adopted the Congregational form of government.  In February, 1817, it united with the Union Association and continued that connection till the dissolution of that body in February, 1822.  The Church adopted the Presyterian form of government in October, 1826, and united with the Presbytery of Chenango at the time of the first meeting of that body after is organization, June 29, 1826.  April 9, 1827, "The Presbyterian congregation of McDonough met at the school-house in district No. 7, for the purpose of organizing an incorporated religious society."  Jonas Herrick was chosen moderator and Samuel W. Knight secretary of the meeting, and Jonathan Proctor, Eliakim L. Corbin, Levi Carruth, Samuel W. Knight and Frederick G. _____, were elected trustees.

10a.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Arian CORBIN; Birth: 05 Nov 1805; Death: 19 Mar 1873 Horace CORBIN; Birth: 10 Dec 1806; Death: 03 Jul 1882 Abel Rathbone CORBIN; Birth: 24 May 1808; Death: 28 Mar 1880 Lavinia CORBIN; Birth: 07 Jul 1810; Death: 26 Dec 1855 Eli Lyon CORBIN; Birth: 07 Feb 1812; Death: 29 Oct 1896 Lucia Amanda CORBIN; Birth: 31 Dec 1821; d. 31 Jan 1878 Father: Eliakim CORBIN; Mother: Lodama RATHBONE Source: patron submissions

Arrian CORBIN, Levina CORBIN, Amanda CORBIN Christening: 17 Aug 1817, Congregational Church, Exeter, Otsego, New York Father: Eliakam L. CORBIN; Mother: Lodamia Source: patron submissions

Harvey CORBIN, Lurin CORBIN Christening: 01 Jul 1806, Exeter, Otsego, New York Father: Eliakam L. CORBIN; Mother: Lodamia Source: patron submissions

Is "Lurin" actually "Arian"?

10b.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs, online at FamilySearch.org). 
There are some discrepancies here compared to the info in the IGI.

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