In his World War I draft registration card, James Sr. is listed as "James Folsom Dickson". (Ancestry.com indexes the middle name as "Falsom", but it looks like "Folsom" to me. Find A Grave also lists his name as "James Folsom Dickson".)
In the 1930 census, the children are listed as Cooper B. (daughter, 19); James F. Jr. (son, 14), G. LeGrande (son, 12), and Lida M. (daughter, 1). ("James F. Jr." appears to be an error for Joseph.)
Here is part of Joseph's obituary from the February 14, 2004 issue of The (Columbia) State newspaper:
"LAKE CITY - Joseph E. Dickson, Sr., 88, of Lake City, S.C., passed away Friday morning, February 13, 2004, in the hospital after a short illness. Mr Dickson was born in Manning, S.C., a son of the late James F. and Alida Fulton Dickson. He was predeceased by his beloved wife Ethelyn Floyd Dickson, a brother Legrande Dickson of Manning, S.C., and two sisters, Cooper Dickson Jones of Manning and Alida Dickson Barton of Springfield, Va. Mr. Dickson was a graduate of Manning High School and attended Furman University. He was a former Sunday School teacher, deacon and elder at the Lake City Presbyterian Church. He was a member of the Kingstree Presbyterian Church. Mr. Dickson was a retired farmer. [...] Survivors include his son, Joe E. Dickson, Jr. and daughter-in-law, Diane Dickson of W. Columbia; daughter, Viva D. Herscher and son-in-law, Dr. Carl Herscher of Mt. Pleasant; four grandsons, Jo Jo Dickson of W. Columbia, Ryan Dickson of Lake City, Marc Herscher of Atlanta and Adam Herscher of Columbia; one great granddaughter, Mackenzie Dickson of Lake City, and a sister, Alice I. Fitzhugh of San Antonio, Texas."
According to the Social Security Death Index, Cooper Jones died January 1974.