The records below are in the correct location for an Alice Williams and ? Solomon Simmons. Maybe you might recognize some of the siblings names as great aunts/uncles from the earlier census data?
US Census, 1940 Jackson Township, Crittenden, AR
C S Simmons Head M 25 Arkansas
Alice Simmons Wife F 24 Arkansas
James A Simmons Son M 6 Arkansas
Vera Jean Simmons Daughter F 4 Arkansas
Christine Simmons Daughter F 2 Arkansas
Gertrude Simmons Daughter F 0 Arkansas
Arkansas, County Marriages, 1837-1957
IMAGE SOURCE: https://familysearch.org/pal:/MM9.3.1/TH-266-11005-103880-23?cc=1417439
Citing this Record: "Arkansas, County Marriages, 1837-1957," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NMDB-ZZW ), C S Simmons and Alice Williams, 11 Apr 1934; citing , Crittenden, Arkansas, United States; FHL microfilm 2110017.
Name: C S Simmons
Marriage 11 Apr 1934 Crittenden, AR
Residence Place: Waverly, Arkansas
Spouse: Alice Williams
Residence Place: Waverly, Arkansas
U S Census, 1930 Proctor, Crittenden, AR
Citing this Record: "United States Census, 1930," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/XM2T-C8N), Alice Williams in household of Louise Williams, Proctor, Crittenden, Arkansas, United States; citing enumeration district (ED) 0022, sheet 10A, family 271, NARA microfilm publication T626, roll 71.
Louise Williams Head F 33 Mississippi
Alice Williams Dau F 14 Arkansas
Mary Bell Williams Dau F 12 Arkansas
Louise Williams Dau F 10 Arkansas
Floyd Williams Son M 2 Tennessee
Mary Williams Mother F 50 Mississippi
US Census 1920, Lucas, Crittenden, AR
Citing this Record: "United States Census, 1920," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MDNX-LG8), Alice Williams in household of Joe Williams, Lucas, Crittenden, Arkansas, United States; citing sheet 13B, family 237, NARA microfilm publication T625, FHL microfilm 1820060.
Joe Williams Head M 34 Arkansas
Louise Williams Wife F 24 Mississippi
Alice Williams Daughter F 3 Arkansas
Mary Williams Daughter F 2 Arkansas
This one’s a long shot, could CS be Charlie Solomon, after his father Charles?
U S Census, 1930 Jasper, Crittenden, AR
Citing this Record: "United States Census, 1930," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/XM2R-YT7), Solomon Simmons in household of Charley Simmons, Jasper, Crittenden, Arkansas, United States; citing enumeration district (ED) 0012, sheet 16A, family 263, NARA microfilm publication T626, roll 71.
Charley Simmons Head M 55 Mississippi
Gertrude N Simmons Wife F 40 Georgia
Solomon Simmons Son M 15 Arkansas
Cathrine Simmons Daughter F 13 Arkansas
U S Census, 1920 Jasper, Crittenden, AR
Citing this Record: "United States Census, 1920," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MDNX-Y6B ), Salmon Simmons in household of Charlie Simmons, Jackson, Crittenden, Arkansas, United States; citing sheet 11B, family 247, NARA microfilm publication T625, FHL microfilm 1820060.
Charlie Simmons Head M 46 Mississippi
Gertrud Simmons Wife F 28 Georgia
Henry Simmons Son M 9 Arkansas
Mary Lue Simmons Daughter F 7 Arkansas
Alevie Simmons Daughter F 6 Arkansas
Salmon Simmons Son M 5 Arkansas
Surline Simmons Daughter F 3 Arkansas