There is nothing known about Peter and Eli Cooper's parent's at this time. But we know that they both arrived about the same time in 1807 in Tennessee.
Sources
Book: Dusty Bits of the Forgotten Past: A History of Scott County, TN p. 8-9 - Settlement of 1807 Clinch River Ferry, List people already living in Scott & Campbell County, TN.
Find a Grave, database and images (https://www.findagrave.com/memorial/54152571/thomas-council-cooper: accessed 25 September 2023), memorial page for Thomas Council Cooper (19 Oct 1762–27 Jul 1849), Find a Grave Memorial ID 54152571; Burial Details Unknown; Maintained by Eli Brown (contributor 47299033).
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DNA Connections
It may be possible to confirm family relationships with Thomas by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Thomas:
It is NOT known who the father of Peter and Eli Cooper who were brothers. They both came to Tennessee together. They are not Thomas Council Coopers son. But they arrived together see uploaded page: https://www.wikitree.com/photo/jpg/Cooper-23126-1