Although I don't have info of my own for this family, I did a bit of surfing around and found them in Rockwood, Randolph County, Illinois, at least between 1860 and 1880. Jackson's full name may have been Andrew Jackson, as per a marriage listing I found in the Illinois Statewide Marriage Index, 1763–1900.
ARNEY, ANDREW JWILLIAMS, SARAH E1862-03-19 A/541RANDOLPH
Also found two Sarah Arney marriage records...timing looks good.
COOK, HARTLEYARNEY, SARAH1865-03-09 B/142RANDOLPH GREENAWALT, WILLIAMARNEY, SARAH C1873-01-01 C/37170RANDOLPH
I also searched the Illinois State archives for military records and found an Andrew Arney, stated age as 23 (close!), who was in the 13th Calvary and who died of illness in 1864, while in Pine Bluff, Ark.
He said he resided in Jones Creek, Il, also in Randolph county.(circa 1860)