Are you sure of Catherine Kendall as second wife with son Samuel 1854?
1850 Census: Walnut, Pickaway, OH Amstrong Jones 35 Delila 24 Wiliam 6 Mary J. 4
1860 Census: Madison, Fairfield, OH Armstrong Jones 44 Delilah 39 Wm 16 Jon W. 9 Ellen 7 SAMUEL 6 Sarah 1
1870 US Census: Madison, Fairfield, OH Armstrong Jones 53 Delilah 45 John 19 Samuel 13 William 264Sarah 11 Jacob 7 Wilda L. 4
It appears this is the same Armstrong Jones family, albeit the ages flutter a bit, but that is genealogy and the census takers!Plus, i often see varient in ages of several years.My husband's grandmother lied about her age (younger by 5 years until she realized seniors have benefits!)
Anyway....IF this is the same Armstrong James family,then Delilah appears to be the mother of a Samuel born abt 1854.
I could not find anything on A's parents.Good luck.