There was a Martha Gibson James, born about 1902 according to her 1955 death certificate. Her parents were Melton Gibson and Amelia Spencer Gibson. She and her parents lived in Sumter Co SC. Is this the family you are looking for?
Melton and Amelia Gibson had a son named Luke born 1886-88,who lived with his mother at least through 1940
Dear Ms. Fordham,
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We searched the National Archives Catalog and located the Population Schedules for the 1890 Census; the Population Schedules for the 1900 Census, and the Population Schedules for the 1910 Census, the Population Schedules for the 1920 Census, the Population Schedules for the 1930 Census, and the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that may contain information about Amelia Gibson and her family. The 1940 Census schedules are digitized and available using the Catalog. For access to the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
For information about the U.S. Census, see the Census Bureau technical documentation and questionnaires.
You may wish to search Ancestry.com or FamilySearch.org for the U.S. Census. There may be a fee for using Ancestry. Instead, please check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
We also suggest that you contact the South Carolina Department of Archives & History to request a record search and review the FamilySearch Research wikis for South Carolina Vital Records, Sumter County, South Carolina Genealogy and African American Resources for South Carolina.
We hope this is helpful. Best of luck with your research!