Sarah is said to have had only two children; otherwise, I would have assumed that all four of the children born before 1840 were hers — and they well may have been.

Is the secondary source wrong?  Did Sarah have four children?  Are these Coleman's children from another wife?  Are they Coleman's children, at all?  None of the four appear in the 1850 census.  The girls were old enough to have married, but the boys were not.  Did they die?

I wonder if Sarah and Viola are really are subjects' children.  Delilah was really too old to be having children in the 1860s.
11.  Sarah WOODWARD, b. 1861/2
12.  Viola WOODWARD, b. 1864/5

1.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):

Woodard, Coleman

Corbin, Delila

1 Jan 1840

Hancock Co.

2.  1840 Census Index and Digital Images (online at Ancestry.com; Image #5-4 of 8, note that pages were numbered and microfilmed in reverse order; extracted by Diana Gale Matthiesen):

1840

OH

Hancock Co.

Marion Twp.

p. 37

Coleman Woodward

200 010 - 020 010

0100000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	4 or under	1835-1840	= Son B = Son A
1 male	20-29	1810-1820	= Coleman (b. 1811/2)
2 females	5-9	1830-1835	= Daughter B = Daughter A
1 female	20-29	1810-1820	= Delilah (b. 1817/8)
1	person engaged in agriculture

3.  1850 Census Index/Images (online at Ancestry.com; Image #5 of 15):  Richland Twp., Wyandot Co., OH, p. 222A/443, 32/821, enumerated 11 Sep 1850 (extracted by Diana Gale Matthiesen):

Coleman Woodward	38	M		Laborer		Va
Delia       "	32	F				Pa
Wealthy E   "	10	F				O
William     "	8	M				"
Benjamin J  "	5	M				"
George W    "	2	M				"
John C      "	1/12	M				"

Living next door to William & Susan (ARCHEBAL) CORBIN.

4.  1860 Census Images (online at Ancestry.com; Image #11 of 38):  Vanlue P.O., Amanda Twp., Hancock Co., OH, p. 202A, PN 11, 85/82, enumerated 4 Jun 1860 (extracted by Diana Gale Matthiesen):

Coleman Woodward	50	M		Farm Laborer		50	Va
Delilah    "	45	F					Pa
Benjamin   "	15	M		Servant			"
John C     "	10	M					"
James L    "	7	M					"
Sarah Ellison	15	F		Servant			O
Josephine  "	3	F					Iowa

The children were born in Ohio, not PA.

5.  1870 Census Images (online at Ancestry.com; Image #2-3 of 32):  Marseilles P.O., Richland Twp., Wyandot Co., OH, pp. 785B-786A, PN 2-3, 17/17, enumerated 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Woodard Coleman	50	M	W	Farmer		200	Va
_______ Benjamin	25	M	W	Farmer			O
_______ Hellen	20	F	W	Keeping house			NY
_______ Delia	43	F	W	Keeping house			O
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Woodard Lafayette	15	M	W	works on farm			O
_______ Sarah	8	F	W				O
_______ Viola	5	F	W				O

The enumerator appears to have royally botched this record, still, how could it be anyone else but our subjects?  Helen is Benjamin's wife (in 1880 census).

6.  1880 United States Census and National Index (LDS Family History Resource File: CD-ROM Library):

Census Place: Forest, Hardin, Ohio
Source: FHL Film 1255030; NARA Film T9-1030; Pg 109A
	Relation	Sex	Marr	Race	Age	Birthplace	Occupation	Fa	Mo
J. L. WOODARD	Self	M	M	W	27	OH	Laborer	VA	PA
Catharine WOODARD	Wife	F	M	W	27	PA	Keeping House	PA	PA
James F. WOODARD	Son	M	S	W	4	OH		OH	PA
Chas. WOODARD	Son	M	S	W	3M	OH		OH	PA
Wm. J. KEGG	BroL	M	S	W	22	OH	Laborer	PA	PA
Delilah WOODARD	Mother	F	W	W	62	PA	At Home	MD	PA

"J.L." is Delilah's son, James Lafayette.  Son, Benjamin, is also in Hardin Co.

7.  Anon.  1896.  A Portrait and Biographical Record of Allen and Putnam Counties, Ohio (reprinted 1984 by Whipporwill Publ., Evansville, IN; excerpt courtesy of Debbie Ritzenthaler).

... Henry and Charlotta (Corbin) Greene ... To them ten children were born, only two of whom are now living.  The children were as follows: Sarah, who married Coleman and died in Hancock county, Ohio, leaving two children...