LEX has Air Lexington (Barons, KAs and a CJ) and I think a company called Global Air Charter...GAC has/had a GIII and a LR55.
LOU has Central American Airways/WL Paris, with a bunch of King Airs and Citations.
SDF has Excel Air (not to be confused with Excelaire); they have 2 Citation Excels.
JVY (southern Indiana) has Aircraft Specialists, with 2 LR35s and 2 King Airs.
Somebody down in OWB has a Citation and/or a Beechjet.
Honaker Aviation in Bardstown has a LR35 I think.
Part 91? There's a bunch all around the state from piston singles through GVs, but most are King Airs or light jets and I don't know of any actively hiring. Usually Yum! posts an opening or two every year in Louisville though.