Hi,

I think I may have found them.

1910 United States Federal Census

Name: James Amster
[James Arnold]
Age in 1910: 32
Estimated birth year: abt 1878
Birthplace: Mississippi
Relation to Head of House: Head
Father's Birth Place: Mississippi
Mother's Birth Place: Mississippi
Spouse's name: Berko
Home in 1910: Griggs, St Francis, Arkansas
Marital Status: Married
Race: Black
Gender: Male

Household Members: Name Age
James Amster [Arnold] 32 Head
Berko (Birtie) Amster [Arnold] 33 Wife
France (Frank) Amster [Arnold] 9 Son
Tomma Amster [Arnold] 7 Son
Fred Amster [Arnold] 5 Son
Laval Amster [Arnold] 5 Dau
James Amster [Arnold] 1/12 Son

I believe that this is Birdie. It says that she died in 1924 in Cross County which is next door to Saint Francis County

Arkansas Death Index, 1914-1950
about Birdie Arnold
Name: Birdie Arnold
Death Day: 24
Death Month: Feb
Death Year: 1924
County: Cross
Roll Number: 19241933

I believe that this is James Arnold in Cross County in 1930 with his second wife.

1930 United States Federal Census

Name: James Arnold
Home in 1930: Tyronza, Cross, Arkansas
Age: 45
Estimated birth year: abt 1885
Birthplace: Mississippi
Relation to Head of House: Head
Spouse's name: Alice
Race: Negro (Black)

Household Members: Name Age
James Arnold 45 Head
Alice Arnold 52 Wife
Willie Arnold 18 Dau
Herman Arnold 12 Step Son

Next door is James Arnold Jr., the son of James Arnold Sr.

1930 United States Federal Census
about James Arnold
Name: James Arnold
Home in 1930: Tyronza, Cross, Arkansas
Age: 20
Estimated birth year: abt 1910
Birthplace: Arkansas
Relation to Head of House: Head
Spouse's name: Lilly
Race: Negro (Black)

Household Members: Name Age
James Arnold 20
Lilly Arnold 17
Betty Arnold 1 7/12

Now, two pages from James Arnold Sr is a Tom and Frank Arnold. I believe that they are James and Birtie's sons. The problem is that Ancestry.com list them as white and the census image list them as white.

1930 United States Federal Census
about Frank Arnold
Name: Frank Arnold
Home in 1930: Tyronza, Cross, Arkansas
Age: 30
Estimated birth year: abt 1900
Birthplace: Arkansas
Relation to Head of House: Head
Race: White

Household Members: Name Age
Frank Arnold 30 Head
Tom Arnold 25 Brother

I could not find any one of them in 1920.

Tony