Given the fact that Adam's birthyear is different in nearly every record given for him, it appears he may not have known the exact year he was born, which was not that unusual for the time.  Either that or we have a case of age inflation, pushing his birthyear back to 1797 on his tombstone.  A birthyear of 1800 is more likely (see 1830 and 1840 censuses).

1.  Marriage Record:

2.  AIS (Accelerated Index System) 1820 Census Index (online at Ancestry.com):  not found in Chanceford Twp., York Co., PA.

3.  1830 Census Index and Digital Images (online at Ancestry.com; Image #3 of 16; extracted by Diana Gale Matthiesen):

1830

PA

York Co.

Upper Chanceford Twp.

p. 470

Adam Kup

000 010 - 200 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	20-29	1800-1810	= Adam
2 females	4 or under	1825-1830	= Margaret (b. 1828/9) = Rebecca (b. 1827/8)
1 female	20-29	1800-1810	= Wife-1

Listed three lines above Michael ARNOLD.

4.  1840 Census Index and Digital Images (online at Ancestry.com; Image #13 of 16; extracted by Diana Gale Matthiesen):

1840

PA

York Co.

Chanceford Twp.

p. 307B?

Cup Adam

110 001 - 112 000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= Jacob (b. 1834/35/36)
1 male	5-9	1830-1835	= John W. (b. 1831/32/35/36)
1 male	30-39	1800-1810	= Adam
1 female	4 or under	1835-1840	= Eve
1 female	5-9	1830-1835	= Annie
2 females	10-14	1825-1830	= Margaret (b. 1828/9) = Rebecca (b. 1827/8)

Elizabeth ARNOLD is supposedly Adam's one-and-only wife, but unless this is census-taker error, he is clearly a widower — and thus had at least two wives.  The youngest daughter, Catherine (b. 1839/40) is missing from the household, but as an infant (whose mother probably died giving birth to her), we would expect her to be in the care of some related woman, most likely his wife's mother or a sister.  The toddlers would be old enough for the older girls to manage, but not an infant, and especially not a newborn.  The other possibility, of course, is that the Adam in 1830 and 1840 is a different Adam than the one in 1850, 1860, and 1880, but that proposition creates worse problems than it solves.  A more viable alternative is that, because of a difficult childbirth, Elizabeth is living with her mother or a sister until she and the baby are stonger.  There are numerous ELIUS's in the neighborhood (daughter Margaret married an ELLIAS).

5.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  Chanceford Township, York Co., PA, p. 243B, 247/256, enumerated 31 Dec 1850 (extracted by Diana Gale Matthiesen):

Adam Cupp	43	M	Labourer	400	Penna
Elizabeth "	48	F			"
John      "	18	M	Labourer		"
Jacob     "	15	M	Ditto		"
Eli       "	1	M			"
Rebecca   "	22	F			"
Catharine "	10	F			"

The children are out of order because this enumerator placed males before females.  The older children are Adam's from his first marriage.  Eli is the only child of Adam & Elizabeth, together.  The nine-year gap between Eli and Catharine supports that there were two wives.

6a.  Census Index:  U.S. Selected Counties, 1860 (Broderbund CD-318):

1860

Coess, Adam

PA

York Co.

Chanceford Twp.

p. 389

6b.  1860 Census Images (online at Ancestry.com; Image #21 of 57):  Chanceford P.O., Chanceford Twp., York Co., PA, p. 390, PN 21, 146/149, enumerated 28 Jul 1860 (extracted by Diana Gale Matthiesen):

Adam Coep/Colp	60	M		Farmer	700	150	Penna
Elizabeth "	49	F					"
John      "	24	M		Laborer			"
Eve       "	19	F		Domestic			"
Catharine "	17	F		"			"
Elijah    "	10	M					"

This enumerator often made his lower case L's very small.  There is a Catharine COLP (age 18, b. PA) enumerated in Chanceford Twp. as living in the household of John ARNOLD (image 52, p. 418).  As a domestic, it is probable that Catherine got enumerated twice, once at home and once in the home of her "employer," who is probably Elizabeth's kin.

7.  1870 Census Index/Images (online at Genealogy.com; Image #51 of 65):  Bald Eagle P.O., Chanceford Twp., York Co., PA, Roll 1468 (Book 1), p. 236B, PN 50, 409/402, enumerated 17 Sep 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Cupp Jacob	34	M	W	Farmer	1200	500	Penna
____ Sophia	26	F	W	Keeping house			"
____ Alfred	10	M	W				"
____ M A	8	F	W				"
____ Catharine	6	F	W				"
____ Elizabeth	3	F	W				"
____ Amos	8/12	M	W				"
____ Adam	72	M	W	Laborer		100	"

8a.  1880 United States Census and National Index (LDS Family History Resource File: CD-ROM Library):

Census Place: Chanceford, York, Pennsylvania
Source: FHL Film #1255208; NARA Film #T9-1208; Pg 618B
	Relation	Sex	Marr	Race	Age	Birthplace	Occupation	Fa	Mo
Benjamin ELLIAS	Self	M	M	W	55	PA	Farmer	PA	PA
Margaret ELLIAS	Wife	F	M	W	51	PA	Keeping House	PA	PA
[Benjamin & Margaret's five children]
John ELLIAS	Brother	M	S	W	72	PA	Laborer	PA	PA
Adams CUPP	FatherL	M	W	W	81	PA	Laborer	PA	PA

8b.  1880 Census Images (online at Ancestry.com; Image #12 of 31):  in checking the image of the above record, it's "Adam," not "Adams," and Margaret's age could just as easily be 37 as 51 (in fact, it looks slightly more like 37 than 51).  As Margaret does not appear in the 1850/60 censuses, the later birthdate would make more sense in that regard, but then, Elizabeth would have been having a child at age 51/2, which is unlikely.  It would help if I could find Benjamin ELIAS in the 1860 census of York Co., but I can't, which increases the probablity that Margaret was his second wife.

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