Eliphaz's mother was Martha Chapman Coffin, who died about 1782, the year of Eliphaz's birth, or Elizabeth unknown Coffin, who Stephen married after his first wife's death.
Sources
COFFIN GATHERINGS: Five Generations of Descendants of Tristram Coffin of Newbury and Nantucket, By W. S. Appleton. Boston: Press of David Clapp & Son, 1896, p 12. [An outgrowth of the anniversary meeting of the Coffin family at Nantucket in 1881.]
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DNA Connections
It may be possible to confirm family relationships with Eliphaz by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
G C :
Family Tree DNA Y-DNA Test 111 markers, haplogroup R-BY34208, FTDNA kit #266234
Chip Coffin :
Family Tree DNA Y-DNA Test 700 markers, haplogroup R-BY60137, Ancestry member Chip_Coffin, FTDNA kit #954106
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Eliphaz: