This is what I could find on James Mooneyham: Most information is from ancestry.com--I am not related, just like helping out when I can.

James J. Mooneyham married Etta Reese
23 Nov 1918 Jackson Co., Arkansas

J. J. Moneyham married Fany Brewer
28 Dec 1919 Craighead Co., Arkansas—lived in town of Monette

J. J. Mooneyham married Jennie Puckett
29 June 1935 Jackson Co., Arkansas

James Mooneyham married Thelma Robinson
26 April 1939 in Woodruff Co., Arkansas-lived Beedeville Jackson Co., Arkansas

1910 census
ED 45 sheet 6A line 33
House 6 of 6 Franklin and Rapier
Big Springs Twsp., Izard Co., Arkansas
April 16, 1910

Daniel, Stephen G. head 34 M1-13 Ar Tn Tn farmer
Mattie J. wife 31 M1-13 Ar Ar Ar 10 children born 5 living
Gracie E. dau 7 S Ar Ar Ar
Laurence J. son 5 S Ar Ar Ar
Lola M. dau 3 S Ar Ar Ar
Theodore R. son 2 S Ar Ar Ar
Miles A. son 4/12 S Ar Ar Ar
Mooneyham, Julia A. Mother 65 WD Tn NC Va
James J. brother 18 S Ar Tn Tn farm laborer
1918 draft record
James Jefferson Mooneyham
Lived Staark, Izard Co., Arkansas
Nearest relative: Mylinda Bone either Pettig or Rettig, Texas
Description: medium height and build with blue eyes and light hair
September 12, 1918 Jackson County Draft Board, Jackson Co., Arkansas
1920 census
ED 139 sheet 30 A line 25
House 119 0f 131 farm
Neal Twsp., Mississippi Co., Arkansas
February 13, 1920

Mooneyham, J. J. head 26 M Ar Tn Tn farmer
Fannie wife 28 M Ar Unk Unk
Lola B. dau 4 S Ar Ar Ar

1930 census---According to your inquiry, you already have this record.
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1940 census
This record is from Ancestry.com
ED 34-15 sheet 5A line 22
House 79 rents
Cow Lake Twsp., Jackson Co., Arkansas
April 10, 1940
Index page 11

Mooneyham, James head 49 M Ar education: 0 farm laborer
Thelma wife 45 M Tn education H-2
Robinson, Dallas s-son 10 S Tn education 3
Thadius s-son 6 S Tn education 0
Marie s-dau 3 S __ education 0
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From: Findagrave.com
Etta Gay Mooneyham
Born: unknown
Died: November 19, 1934
Buried: EightMile Cemetery-Beedeville, Jackson Co., Arkansas