Based on the family bible, two children were born on 17 Jan 1871, but the image is so faded I can't read their names — and one name does appear scratched out.

1a.  Missouri Marriage Records.  Missouri State Archives, Jefferson City, MO (online at Ancestry.com):

Mr John Davis

Miss Nancy Rouse

13 Mar 1870

Boone Co.

An image of the marriage book page is online at Ancestry, but it's essentially unreadable.  It looks like it might have information on it that would make it worth the effort to seek out a better microfilm.

1b.  Arkansas County Marriages, 1837-1944 (online at familysearch.org):

Groom's Name:	John C. Davis
Groom's Age | Est. Birth Date:	43 | 1845
Bride's Name:	Lockie L. Weir
Bride's Age | Est. Birth Date:	32 | 1856
Marriage Date:	02 Feb 1888
Marriage Place:	Cleburne, Arkansas
Bride's Marital Status:	Unknown
Source Film:	1033446

1c.  Arkansas County Marriages, 1837-1957 (online at familysearch.org):

Name:	Jno C Davis
Event:	Marriage
Event Date:	02 Feb 1888
Event Place:	Cleburne, Arkansas, United States
Age | Est. Birth Year:	43 | 1845
Residence:	Hiber, Cleburne, Arkansas
Spouse:	Lockie L Wern
Spouse's Age | Est. Birth Year:	32 | 1856
Spouse's Residence:	Hiber, Cleburne, Arkansas
Marriage License Date:	02 Feb 1888
Page:	258
Digital Folder:	004326281

2.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  John DAVIS (æ 8, b. MO) is living in Dist. No. 8, Boone Co., MO, with his widowed mother (q.v.).  Nancey ROUSE (æ 1, b. MO) is living in Dist. No. 8, Boone Co., MO (p. 364A), with her parents, Alfred ROUSE (æ 45, b. KY) & Mahala (æ 30, b. KY), plus siblings; they are listed next to widow Sarah (FRENCH) FRENCH, daughter of Mary (CLARK) FRENCH, who is sister of our subject's paternal grandmother, Sarah (CLARK) DAVIS.

3.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  John DAVIS (æ 18, b. MO) is living in Rockyfork Twp., Boone Co., MO, with his widowed mother (q.v.).  Nancy ROUSE (æ 10, b. MO) is living in Rocky Fork Twp., Boone Co., MO (p. 645), with her parents, Alfred ROUSE (æ 57, b. KY) & Mahala (æ 47, b. KY), plus siblings; they are listed two households from Benjamin F. & Sarah J. DAVIS. 

4.  1870 Census Every-Name-Index/Images (online at Ancestry.com):  can't find the newlyweds.  Widow Mahala ROUSE (æ 50, b. KY) is living in Boone Co., MO (p 226B), with her children.

5.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #12 of 27):  Wilson Twp., "South the the C & R R," Audrain Co., MO, Roll 672, p. 200D, PN 12, SD 3, ED 9, enumerated 10 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

7

8

9

10

13

21

24

25

26

105

110

Davis John

W

M

38

/

Farmer

Mo

Ky

Ky

_____ N C

W

F

28

Wife

/

Keeping house

Mo

Ky

Ky

_____ L E

W

F

9

Dau

/

/

Mo

Mo

Mo

_____ L B

W

M

5

Son

/

Mo

Mo

Mo

_____ J Smith

W

M

4/12

Jan

Son

/

Mo

Mo

Mo

6.  1890 Census:  the 1890 Census Population Schedules were destroyed.

7.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #1 of 12):  South Sugar Loaf Twp., Cleburne Co., AR, Roll 54, p. 271A, SN 7, SD 2, ED 19, enumerated 7 Jun, 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

22

23

24

25

26

27

28

128

128

Davis Lockey L

Head

W

F

Mar 1857

43

Wd

6

4

TN

TN

TN

Y

Y

Y

O

F

F

30

_____ William

Son

W

M

Aug 1876

23

S

KY

TN

TN

Farmer

0

Y

Y

Y

_____ Smith

Son

W

M

Jan 1879

21

S

MO

TN

TN

Y

Y

Y

_____ Emmet C

Son

W

M

Mar 1891

9

S

AR

TN

TN

N

N

Y

_____ Richard B

Son

W

M

Sep 1895

4

S

AR

TN

TN

N

N

Y

William WIER-DAVIS is Lockey's son from her prior marriage; William's father was born in KY.  The father of the three DAVIS boys (our subject) was born in MO.  Smith DAVIS is Lockey's stepson; his mother was born in MO.  A family bible says that Smith was born in Jan 1880, that Emmitt was born in Mar 1890, and that Richard was born in Oct 1896.

8.  1910 Census Every-Name-Index/Images (online at Ancestry.com, Image #1 of 15):  Private Road, Heber Twp., Cleburne Co., AR, Roll 46 (Book 2), p. 90A, SD 2, ED 9, enumerated 15 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):

1910:  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	10	11	12	13	14	17	18	19	20	21	22	23	24	25	26	27	28	29
3	3	Davis Lockey Mrs	Head	F	W	54	Wd	10	6	4	TN	TN	TN	Eng	House work			N	0	Y	Y		O	F	F	3
		Weir William	Son	M	W	33	S				KY	KY	TN	Eng	Farm	Farm	OA	N	0	Y	Y
		Davis Clark	Son	M	W	20	S				AR	MO	TN	Eng	Laborer	Farm	Emp	N	0	Y	Y
		_____ Bryon	Son	M	W	13	S				AR	MO	TN	Eng	None					Y	Y	Y

Listed three households from son Emmitt Clark's future wife, Mary L. HALBERT, and her parents.

9.  1920 Census Every-Name-Index/Images (online at Ancestry.com):  Lockie L. DAVIS (æ 67, b. KY) is living in Heber Twp., Cleburne Co., AR (p. 265A), with her married son, William T. WEIR (æ 42, b. KY).

10.  1930 Census Every-Name-Index/Images (online at Ancestry.com):  Lockey not found.

11.  CADI:  California Death Index, 1940-1997 (online at RootsWeb.com):

Last Name	First Name	Middle	Birth Date	Mother Maiden	Father Last	Sex	Birth Place	Death Place (County)	Death Date	SSN	Age	Post-em Placed
-	-	-	-	-	-	-	-	-	-	-	-	No
DAVIS	Leonidas	Brown	01/15/1875	ROUSE	DAVIS	M	MO	Los Angeles (19)	01/27/1943	549-03-5891	68	No
-	-	-	-	-	-	-	-	-	-	-	-	No
-	-	-	-	-	-	-	-	-	-	-	-	No

12.  SSDI:  Social Security Death Index (online at Ancestry.com):

Name	Birth	Death	Last Residence	SSN	Issued	Comment
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No
-	-	-	-	-	-	No

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

14.  Email from descendant, including an image of the "Births" page from what appears to be our subject's Family Bible.  The handwriting is very difficult to read, and some entries are badly faded.  Only Lockey is missing.  Unfortunately, I cannot make out the names of the twins born 1871, nor can I make out Smith's first name, which appears abbreviated (Jas? Jos? Jno?).