— born in Sullivan Co., MO:
  8.  James Edward DAY, b. 13 Apr 1859; d. 1907
  9.  Martha Grace DAY, b. 22 Jun 1861; d. 20 Dec 1862; bur. Wintersville Cem.
10.  Mary R. DAY, b. 11 Dec 1862; d. 1863; bur. Wintersville Cem.

Surely Rebecca and Peyton were born in the same day.  Peyton had to have died before the 1860 census.

1a.  Illinois Statewide Marriage Index, 1763–1900 (online at the Illinois State Archives web site):

Day, Franceway (date in doubt)

Chapman, Harriet (return blank)

1840-00-00

Vol. A, p. 23

Lic #133

Menard Co.

It's possible they got a license, then never followed through with the ceremony, which would be consistent with Franceway not showing up in the 1840 census and with the fact that they apparently had no children.

1b.   Iowa: County Marriages, 1838-1934 (online at familysearch.org):

Franceway Day	Mary Ann Noble	22 Mar 1849	Jefferson Co.	GS Film #969379	Ref ID BkB P152 cn587
Franceway Day	Elizabeth J. Robinson	25 Mar 1865	Keokuk Co.	GS Film #1005838	Ref ID 192A

2.  1840 U.S. Census Index/Images (online at Ancestry.com):  Franceway not found, but his father, Will DAY (æ 50-60), is living in Menard Co., IL (p. 306B).

3.  1850 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #49 of 115):  District No. 20, Keokuk Co., IA, Roll M432_185, p. 247A, 337/356, enumerated 10 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Franceway Day	36	M		Phisician	600	[unreadable]
Mary A Day	22	F				Penn
Wm N Day	4/12	M				Iowa

4.  1860 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #1 of 1):  Wintersville P.O., Wintersville, Sullivan Co., MO, Roll M653_658, p. 630, PN 10, 68/68, enumerated 18 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

France way Day	45	M		physician	1800	800	Kentucky
Mary        "	34	F					Illinois
Noble       "	9	M					Iowa
Sarah       "	7	F					do
Sonora      "	7	F					do
Dithey      "	5	F					do
Samuel      "	4	M					Missouri
James       "	1	M					do

Sarah's out of order.

5.  1870 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #14 of 22):  Milan P.O., Clay Twp., Sullivan Co., MO, Roll M593_823, p. 183B, PN 14, 93/93, enumerated 20 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Day Franciway	55	M	W	Physician & Farmer	2000	1800	Kentucky
___ Elizabeth J	52	F	W	Keeping House		250	"
___ Lenora E	18	F	W	at Home			Iowa
___ Dorthy J	16	F	W	"			"
___ Sarah E	15	F	W	"			"
___ Samuel S	15	M	W	"			"
___ James E	11	M	W	"			Missouri
Robinson Joseph A	16	M	W	"			Indiana

Joseph is Elizabeth's son from her prior marriage.

6.  1880 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #20 of 22):  Clay Twp., Sullivan Co., MO, Roll 738, p. 225D, PN 20, SD 5, ED 203, enumerated 18 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

8

9

10

13

24

25

26

183

183

Day Franseway

W

M

65

/

Physician

KY

VA

KY

___ Elizabeth

W

F

63

Wife

/

Keeping house

KY

KY

KY

___ Senora

W

F

27

Dau

/

At home

IA

KY

PA

Lasure Franceway

W

M

9

Adopted

/

At school

MO

VA

IN

McDaniel James

W

M

22

Boarder

/

Works on farm

MO

KY

KY

Listed next to married son, Samuel DAY.

7.  1890 U.S. Census:  the 1890 Census Population Schedules were destroyed.

8.  1900 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #27 of 43):  Benton Twp., Keokuk Co., IA, Roll 441, p. 24B, SN 14, SD 6, ED 40, enumerated 18 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

9

11

12

13

14

15

19

20

21

22

23

24

25

26

27

28

321

321

Street William E

Head

W

M

May 1840

60

Wd

IN

KY

KY

Farmer

0

Y

Y

Y

O

M

F

63

______ Cora A

Dau

W

F

Feb 1880

20

S

IA

IN

IA

Y

Y

Y

______ Kate

Dau

W

F

Mch 1883

17

S

IA

IN

IA

Y

Y

Y

______ Glenna? M

Dau

W

F

Nov 1886

13

S

IA

IN

IA

8

Y

Y

Y

Day Elizabeth J

Mother

W

F

Dec 1818

81

Wd

5

3

KY

KY

KY

Y

Y

Y

9.  Find-a-Grave: Entries (online at findagrave.com):

Name	Francis Day	Mary Ann Day
Birth	1814	6 Jun 1829
Death	1896	14 Dec 1862
Burial	Wintersville Cemetery Sullivan Co., MO	Wintersville Cemetery Sullivan Co., MO
Spouse	*	*
Contributor	humphreysetc, 11 Mar 2012	humphreysetc, 11 Mar 2012
Memorial #	86632642	86632604

*I linked them 18 Jul 2014.  Some of the children are also buried there.
Does his tombstone really say, "Francis," not Franceway?

10.  United States Veterans Administration:  Payment Cards, 1907-1933 (online at familysearch.org):

11.  United States Mexican War Pension Index, 1887-1926 (online at familysearch.org):

12.  Public Member Trees (online at Ancestry.com).

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

14.  Messages posted to the Day Family Genealogy Forum (online at GenForum.com).

15.  Messages posted to the Day Surname Board (online at Ancestry.com).