Certainly invented well before jets. May try Kettering and the drone aircraft late in WW I. Probably also turns on the definition of autopilot. Believe single axis automatic stability was attempted very early (pre The Brothers) by various inventors. Sperry with gyros would be needed for a wing leveler and a heading hold systems with selectable heading would go with some control in the vertical to produce a true autopilot. IIRC in B-17/24s the autopilot feature was a limited authority heading control system to allow the bombadeer (or bomb aimer if you are British) to control the aircraft from the IP to the target.
Or was it a New Zelander named Pearse who built one out of old tractor and sheep parts (two things there were a lot of on New Zeland farms) but never got proper credit?