The families were of Peacocks, Washington Co., GA, on the FamilySearch database of the 1880 Census, DUNHAM:

Elija, 76, CT CT CT; wf. Eliza, 69, GA GA GA.

Ralph, 35; Katherine, 30; ch. Anna, 13; William, 11; Thomas, 9; Ella, 7; Charlie, 4; & Laura, 1; also in household, "other" Wm. PULLUM, 16; all births in Georgia.

George, 26; wf. Eliza, 23; ch. Pierce, 3, & Fannie, 2, all births in GA.

These were consecutive entries on the census, so Ralph and George must have been the sons of Elija. Possibly the wives gave the census information and didn't know that the father of Ralph and George was from Connecticut.

Do you know the significance of the name Pierce?

I don't think that Bangs or Royal DUNHAM had an Elijah. The vital records of Mansfield, CT, covering the time that Bangs DUNHAM was having children have been published. Bangs DUNHAM, b. 16 Feb. 1751/2, m. 9 Dec. 1782, Mansfield, Submit PHELPS, & had Abel, b. 29 Aug. 1783; Royal, b. 18 Je. 1785, Hannah, b. 3 S 1787; Artemus, b.19 May 1790; & Ella, b. 25 May 1794. I think that the son Abel was the one that m. 6 Je. 1805, Mansfield, Sarah LAMB. Royal DUNHAM, b. 1785, married 27 Aug. 1807, Mansfield, Pamela LAMB, & m2. 28 Oct. 1811, Mansfield, Abiah LAMB. Thus, the children of Bangs were born earlier, and the next generation didn't have any children by 1804.

A Google search for Asahel DUNHAM of Mansfield, CT, will bring up the DUNHAM census entries for Connecticut, 1810, which shows many males of the right age, sons aged under ten.

I don't see any Gerusha in my records, but there were several Jerushas in the DUNHAM family.

Can you think of any other clues?