The only reason for linking her tentatively as a daughter of James Wallace Brown and Nancy Ann Auxier is that she was living next door to Harvey Brown, and some other people’s online family trees link Harvey as their son. It is likely that she is Harvey’s sister, but they may both actually have different parents.

1850 census of Morgan Co., Ky, lists as family #33:
Brown, Amanda, 36; Elizabeth, 15; Mary, 8; Permelia, 6; James, 3. All born in Ky.
The family of Harvey Brown and Huldah Cassity is next door at #32.

1860 census of Morgan Co., Ky, West Liberty, enumerathed 7 July, lists on p. 50 as family #301/298:
Isaac W. Hardin, 23; Mary J., 18; Amanda Brown, 40; Permelia B., 16; James H., 14. All born in Ky.

1870 census of Morgan Co., Ky, West Liberty precinct, lists as family # 173/175:
Hardin, Isaac N., 33, farmer; Mary J., 29; Malinda, 6; Vaughn, John, 11; Brown, Amanda, 52.

For quite some time I had Amanda entered as the widow of an unknown Brown husband, with the notes that her husband was likely to be a son of James Wallace Brown and Nancy Auxier, since Amanda was living next door to Harvey Brown and Huldah Cassity in 1850, but that I could not find any marriage record for a Brown groom to a bride named Amanda in the appropriate time frame in Morgan, Fleming, Carter or Bath county.

When Ancestry.com posted images of all the Kentucky death records from 1911 through 1953 online, though, I found the death certificate of her daughter Permelia, which gave her mother’s maiden name as Amanda Brown, and her father’s surname as Wilson, given name unknown. So now I am linking Amanda herself in as a probable daughter of James Wallace Brown.

(I suspect Isaiah Wilson of being the father of her children, but have no real evidence. Just that he was in the right age range (born ca 1812), and that his son Jerry was known to have fathered several children by women other than his wife, so perhaps “like father like son.”)