— born in Bloom Twp., Fairfield Co., OH:
  4?  Catharine CUPP, b. ca. 1807, OH; m. Simon VAN HORN
  5.  Julianna/ Julia Anna M. CUPP, b. 23 Feb 1809, OH; m. Peter DUNKLEBERGER
  6.  Conrad CUPP III, b. ca. 1811, OH; m. Sarah Ann KESTER
  7?  Mary CUPP, b. ca. 1813; m. John FAHL
  8.  Anna "Nancy" CUPP, b. 10 May 1815; m. Andrew S. STRAUB
  9.  Jacob CUPP, b. 27 Oct 1817, Bloom Twp., Fairfield Co., OH; m1. Dorcas Ann SMITH; m2. Sarah Adaline WHITE
10.  Hester / Esther Ann CUPP, b. 6 Oct 1819; m. Jacob H. SHAFFER

The rest are almost certainly our subjects' children based on circumstantial evidence, which includes...
•  After the death of Peter, his daughter, Rebecca, was living with Jacob and his wife.
•  Julia married the widowed father of Elizabeth's husand.
•  Julia and Conrad are listed next to each other in the 1840 census. 
•  Julia and Hester are listed next to each other in the 1850 census.

1.  Marriage Record:

2a.  Cynthia Herrin, ed.  1999.  Fayette County, Pennsylvania, Vital Records to 1890.  Ancestry, Inc., Orem, UT (online at Ancestry.com).
2b.  Cynthia Herrin, ed.  1999.  Morrow County, Ohio, Vital Records 1830-93.  Ancestry, Inc., Orem, UT (online at Ancestry.com).

Name:	Cupp, Conrad	Cruninger, Elizabeth
Birth Date:	1778	1784
Birth Place:	Pennsylvania	Pennsylvania
Father's Name:
Mother's Name:
Spouse:	Elizabeth Cruninger	Conrad Cupp
Marriage Date:	1805	1805
Marriage Place:	Pennsylvania	Pennsylvania
Children:	Hester and others	Hester and others
Date of Death:	before 1880	before 1880
Place of Death:	Crawford Co., OH	Crawford Co., OH
Occupation:	Farmer

I believe we have been led astray by this compilation.  I have found zero evidence that "our" Conrad was born in Fayette Co., PA, or that he ever lived in Morrow Co., OH, or that he lived or died in Crawford Co.  There were CUPPs in Fayette Co., PA, and earlier, in Westmoreland and Somerset Cos., but they don't appear to have been "our" CUPPs. There is no doubt, whatsoever, that our Conrad KOP/KOPP/CUPP is the one who married Elizabeth KRONINGER, and she is from Northampton [now Lehigh] Co., PA, where we find baptisms of two of their children and where we find both an older Conrad KOP/KOPP, his presumed father, who was closely associated with Elizabeth's father, Daniel KRONINGER, as an executor on Daniel's will, along with Elizabeth's brother, John KRONINGER.  Conrad & Elizabeth must have been married by early 1801, not in 1805, because son Peter was baptised in 1801 in PA (see below).

3a.  Pennsylvania Births and Christenings, 1709-1950 (online at familysearch.org):

Name:	Peter Kopp	Elisabeth Kopp
Gender | Race:	Male	Female
Event Type:	Christening	Christening
Event Date:	27 Dec 1801	09 Jun 1805
Event Place:	Christ Union or Reformed Church Lower Saucon Twp, Northampton, PA	Reformed Church Lowhill, Lehigh, PA
Father's Name:	Conrad Kopp	Conrad Kopp
Mother's Name:	Elisabeth	Elisabeth
GS Film Number :	20350	941099

3b.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

JACOB CUPP Birth: 27 Oct 1817, Blum Twp, Fairfield, Ohio Father: CONRAD CUPP; Mother: ELIZABETH KRONING Source: [patron submission]

3c.  Original fraktur of Anna's birth, which reads:

"Anna Kop was born in the year 1815, May 10 at 11 am in the sign of Blum Township, Fairfield County in the State of Ohio.  She was baptised by Pastor Leist.  The sponsors are Henrich Schmitt and Garth [?].  The parents are Conrad Kop and his wife Elisabethh, Daniel Kroninger's daughter."

4.  1810 U.S. Census Index/Images (online at Ancestry.com):  not found, but the 1810 Ohio census was lost (except for Washington Co.).

5.  1820 Census Index and Digital Images (online at Ancestry.com; Image #4 of 7 — mis-indexed as being in Rush Twp.; extracted by Diana Gale Matthiesen):¤•

1820

OH

Fairfield Co.

Bloom Twp.

p. 108A

Coonrod Cup

111101-42201-0-100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1810-1820	= Jacob (b. 1817)
1 male	10-15	1804-1810	= Conrad III (b. 1809/10)
1 male	16-18	1801-1804	= Peter? (b. 1800/1/2)
1 male	19-25*	1794-1801	= duplicated
1 male	45 or over	in or bef. 1775	= Conrad II (b. 1781)
4 females	9 or under	1810-1820	= Hester (b. 1819) = Anna "Nancy" (b. 1815) = Mary (b. ca. 1813) = Elizabeth (b. 1810-15)
2 females	10-15	1804-1810	= Julia (b. 1809) = Catharine (b. ca. 1807)
2 females	16-25	1794-1804	= ? = ?
1 female	45 or over	in or bef. 1775	= Elizabeth (b. 1782)
1	person engaged in agriculture
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25, which means any individual in column three is duplicated in column four.  So, for an accurate representation of the household, the number in column three should be subtracted from the number in column four.

Both Conrad and Elizabeth are tallied in the wrong column, but surely these are our subjects. 

6a.  Census Index:  U.S. Selected Counties, 1830 (Broderbund CD-315):  not found.

6b.  1830 U.S. Census Index/Images (online at Ancestry.com):  not found.

7a.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  not found.  There is a much younger Conrad CUPP in Perry Co., OH.

7b.  1840 U.S. Census Index/Images (online at Ancestry.com):  not found.

8.  Fairfield County, OH, CUPP Grantee Land Records  (online at Lynn Cupp's web site [link died]):

Grantee	Grantor	Instrument	Date	Book	Page
Conrod CUP	John/Mary RITTER	Deed	1825	O	84
Conrod CUP	Thomas/Lidia CURTS	Deed	1825	O	85

Conrad was the earliest CUPP to buy land in the county.  The second was Valentine CUPP in 1830.

9.  Adjutant General of Ohio.  nd.  Roster of Ohio Soldiers in the War of 1812. Transcription of 1916 (online at the Ohio Historical Society web site).  The text was digitized with OCR (optical character recognition) software and contains the many mistakes typical of that process.

Roster 7, p. 33

Pages 189-190. ROLL OF CAPT. ROBERT REID'S COMPANY. (Probably from Delaware County.) Served from July 28, until Sept 6, 1813. Sergt. _____ Missamore... Privates... Cup, Phillip... Cupt, Conrad...

Almost certainly, "Cupt" was a mistake in OCR.  Philip and Conrad are believed to be brothers — their Sergeant may have been Philip's father-in-law.

10.  Anon.  1880.  History of Morrow County, Ohio.  O.L. Baskin & Co., Historical Publishers, Chicago (online at Heritage Pursuit).  On p. 556, under the heading, "Gilead Township":

JACOB H. SHAFER, farmer and stock-raiser; P.O. Cardington; was born in Delaware, now Morrow Co., Ohio, about the year 1815, and lived there until he was 25 years of age; he then moved to Marion Co. and farmed there for fourteen years; thence to Cardington, where he followed teaming and farming, until 1868, when he came to his present place, and has lived there since.  Nov. 24, 1841, he married Miss Hester Ann Cupp; she was born in Pickaway Co., and moved to Crawford Co., and lived there until she was 17 years old [1836/37], when she went to Delaware Co., and lived there until her marriage... Mrs. Shafer's parents, Conrad and Elizabeth (Cruninger) Cupp, were natives of Pennsylvania; they married there, and moved to Pickaway Co. at an early day, and in 1824, they moved to Crawford Co., where they died.

Based on Delaware County marriage records, they were married in 1842.  Hester was born in Fairfield County, not Pickaway.  I have found no evidence that Hester's parents were ever in Pickaway or Crawford Co.  With certainty, Conrad bought land in Fairfield County in 1825, so he had not left the county in 1824 as stated. If Jacob was the informant for this biographical sketch, which he most likely was, it's not uncommon for spouse's to have significant mis-conceptions about their in-laws.

12.  Richard D. Croninger.  Groningers, Croningers, Chroningers, Greningers, and Kroningers in America.

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