I took a look at those two censuses, and in 1870 it looks like your ancestors had a 15-year old son, and an 11-year old daughter, both of whom would have been alive in 1860.
I did find this family in 1880 for you, still living in the same area:
1880 United States Federal Census > Tennessee > Bledsoe > All Townships > District 1 > Page 4
Dwelling 60/Family 69
James M Smith, white, male, 54, head, married, Farmer, b Tenn, parents b Tenn
Catherine, white, 48, wife, keeping house, b Tenn, parents b Tenn
Andrew J., white, 19, son, works on farm, attended school, b Tenn
James T., white, 16, son, works on farm, attended school, b Tenn
Sarah A., white, 14, daughter, at home, attended school, b Tenn
Minnie A., white, 5, daughter, attended school, b Tenn
Dwelling 61/Family 70
George W Smith, white, male, 2?, head, farmer, he and parents b TN
Margaret P, white, female, 19, wife, keeping house, b Tenn, father b NC, mother b Tn
Arthur, white, male, 3, son, b Tenn
There is another Smith family listed just before them.You can view this for yourself (for free) at ancestry.com
I would recommend working backwards.See if you can find this family in the 1900 census, or further pinpoint when the adults may have died.Their death certificates (if available) will give you the maiden name of Catherine (and hers should give you the names of her parents).Death certificates of their children should also give you Catherine's maiden name.