I'm happy that the above information was useful and sooo productive. Hopefully the following will be of some help.
I'm not saying that this is definitely your family, but it looks like a good match. In my census index, Heritage Quest, it only indexes the heads of households or those within the household that have a different surname. I put in the parameters of surname, place of birth, and state of census and found only the following that satisfied those parameters.
1880 Census: Dayton, Campbell County, Kentucky (across the river from Cincinnati, Ohio)
Harrison, A, white, male, 52, works in ship yard, b. NY, NY, NY
Elizabeth, white, female, 50, wife, b. KY, SC, KY
Wm R, 18, dau (line drawn through this), single,
works in rope walk (work?)b, KY, NY, KY
Capitola, white, female, 15, daughter, single, works
in rope walk (work?) b. KY, NY, KY
Luellen, white, female, 12, daughter, single, at
school, b. KY, NY, KY
Bessie, white, female, 6, daughter, single, b. KY, NY,
KY
Southall, C.B. 23, white, female, daughter, widow, servant b.
KY, NY, KY
H. W. 5, white, male, 5, grandson, b. KY, NY, KY
Edna L, white, female, 2, grandaughter, b. KY, NY, KY
1870 Census: Dayton, Campbell, Kentucky
Harrison, Ananias, 44, male, white, laborer, b. NY
Elizabeth, 40, female, white, keeping house, b. KY
Josephine, 16, female, white, at school, b. KY
Belle, 14, female, white, at , b. KY
William, 8, male, white, b. KY
Capitola, 5, female, white, b. KY
______, 2, male, white, b. KY
1860 Census: Newport, Campbell, Kentucky
Harrison, Ananies, 34, male, ship carpenter, $100 personal
estate, b. NY
Elizabeth, 30, female, b. KY
Josephine, 7, female, b. KY
Felecita (Calista Belle?) 4, female, b. KY
Henry Clay, 8/12, male, b. KY
Arnold, Cornelia, 66, female, b. Virginia
If you go to
www.usgenweb.com and click on Kentucky, then Campbell County, there is a marriage of Calista B (Belle) Harrison to Alex J Southall around 1874. Calista can be found in the 1900 census under the name of "Bower" and she is again a widow.
1900 Census: Ward 1-2, Dayton, Campbell, Kentucky
Bower, Belle C, head, white, female, b. Nov 1855, 44, widow,
mother of 7 children, 6 children living, b. KY, NY,
KY, janitrix, can read, write, spks Eng, rents home
Erwin, son, white, male, b. July 1885, 14, single, b. KY,
OH, KY, at school, can read, write, spks Eng
Robert M, son, white, male, b. Aug 1888, 11, single, b.
KY, OH, KY, at school, can read, write, spks Eng
Ida M, dau, white, female, b. July, 1894, 5, single, b.
KY, OH, KY, at school, spks Eng
next page
Bower, Mitchell S, son, white, male, b. Feb 1898, 2, single, b.
KY, OH, KY
Virginia L, dau, white, female, b. June 1899, 11/12,
single, b. KY, OH, KY
Southall, Henry V, son, white, male, b. Sept 1875, 24, single,
b. KY, VA, KY, house painter, can read, write, spks
Eng
The actual image can be viewed free at
http://pilot.familysearch.org/recordsearch/start.html#p=0 