Amy,
There isn't a 1890 Census, the closest you can get to any type of records is the City Directory right now, however the 1890 Tax List has been transcribed and due to funds, the Society will probably be advertising it as a prepublication sale item.
But for now, the following KENNEDY listings in the City Directory are:
Kennedy, A. F., city assessory City Building, res 621 Center
*Kennedy Rev. P. H. res 927 Clay
Kennedy Robt. laborer res n s Washington
*Kennedy Robt. tobacco stemmer, bds 732 2nd
Kennedy Stephen A. railroader, res 1128 Washington
Kennedy Valora, spinner, wks Henderson Cotton Mills
Probably not much help but am hoping one of these names rings a bell.
Netta, VP, Henderson Co. Historical & Genealogical Society