It's unusual for a woman to inflate her age, but Mary is older in the 1850/60/70 censuses than she was in the 1830/40 censuses, and a younger age at first marriage would make more sense.  Or did James marry a second time, between 1840 and 1850, to a different, older Mary?  Mary is said to have died in 1884, but I cannot find her in the 1880 census.

Said to have this son, but without knowing his age, I can't place him in the above sequence; he could be either of the two apparent survivors, most likely the eldest one (Son A).
.  John KARNS

1.  Marriage Record:

2.  1820 Census Index/Images (online at Ancestry.com; Image #4 of 4; extracted by Diana Gale Matthiesen):

1820

PA

Venango Co.

Rockland Twp.

Roll M33_114

p. 14A

Ln. 20

James Carns

000100-00000-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	19-25*	1794-1801	= James (b. 1795/6)
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25; therefore, any individual in column three is duplicated in column four.  By subtracting the number in column three from the number in column four, you can create an age class "19-25."

Listed one line below Adam CARNS (510010-21010-00), who is four lines below Daniel, then Peter, then John STROUP.

3.  1830 Census Index/Images (online at Ancestry.com, Image #5 of 10 — list was roughly alphabetized; indexed "Herns"; extracted by Diana Gale Matthiesen):¤•

1830

PA

Venango Co.

Richland Twp.

Roll 164

p. 43

Ln. 13

Kerns James

220 001 - 100 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	4 or under	1825-1830	= Isaac Adam (b. 1828/9) = Son B
2 males	5-9	1820-1825	= William (b. 1823/4) = Son A
1 male	30-39	1790-1800	= James (b. 1795/6)
1 female	4 or under	1825-1830	= Eliza (b. 1826)
1 female	20-29	1800-1810	= Mary (b. 1797/9?)

4.  1840 Census Index/Images (online at Ancestry.com, Image #7-8 of 8; extracted by Diana Gale Matthiesen):¤•

1840

PA

Venango Co.

Pine Grove Twp.

Roll 497

pp. 93B-94A

Ln. 12

James Karns

211 200 100 - 111 001

0100000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	4 or under	1835-1840	= Jacob (b. 1837/8) = James (b. 1835/6)
1 male	5-9	1830-1835	= Son C
1 male	10-14	1825-1830	= Isaac Adam (b. 1828/9)
2 males	15-19	1820-1825	= William (b. 1823/4) = Son A
1 male	40-49	1790-1800	= James (b. 1795/6)
1 female	4 or under	1835-1840	= Sarah (b. 1839/40)
1 female	5-9	1830-1835	= Clarissa (b. 1830)
1 female	10-14	1825-1830	= Eliza (b. 1826)
1 female	30-39	1800-1810	= Mary (b. 1797/9?)
1	person employed in agriculture

5.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #9 of 17 — indexed "Karnes"):  Pinegrove Twp., Venango Co., PA, Roll M432_832, p. 78A, 62/62, enumerated 23 Sep 1850 (extracted by Diana Gale Matthiesen):¤•

Jas Karns	54	M		Far	1000
Mary	53	F
Isaac	21	M
Jacob	12	M
Jas	14	M
Sarah	10	F
Henry	8	M

The birthplaces were blank, which presumably indicates Pa.  Listed next to presumed son, William KARNS (æ 26, wife Jane).  There is a Clarissa NICKLESON (æ 20, b. PA), living in Cornplanter Twp. with her husband, James NICKLESON (æ 23, b. PA).  There's no Adam KARNS/etc. in Venango County and no John KARNS/etc. the right age to be our subject's son.

6.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #10 of 22):  Fertig P.O., Pinegrove Twp., Venango Co., PA, Roll M653_1189, p. 409, PN 132/3, 867/867, enumerated 6 Aug 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Jas Karns	65	M		Farmer	1100	300	Pa
Mary  "	61	F					"
Sarah "	19	F		House Keeper			"
Henry "	17	M		Farmer			"

Listed between presumed sons, William S. KARNS (æ 38, b. PA, wife Jane) and Adam KARNS (æ 31, b. PA, wife Ann).  There's no Isaac KARNS/etc. in Venango County.

7.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #19 of 23):  Porterfield P.O., Pine Grove Twp., Venango Co., PA, Roll M693_1460, p. 471A, PN 19, 138/124, enumerated 15 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Karns James	74	M	W	Farmer	1000	713	Pennsylvania
_____ Mary	71	F	W	Keeping house			Pennsylvania
Swab James	16	M	W	Works on farm			Pennsylvania
Madocar? Elisabeth	10	F	W				Pennsylvania

8.  1880 Census Every-Name-Index/Images (online at Ancestry.com):  can't find Mary.  Did she really die in 1884?

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