The best replacement for rider is addendum.

The best alternatives to rider are rated as following:
★★★★★  addendum
★★★★★  spawn
★★★★★  iona
★★★★  bowman
★★★  archer
★★★  rowan
★★  marist
★  daishocker
★  dai shocker
★  drexel
★  ultraman
★  super sentai
★  endorsement
★  zero turn
★  line flyer
★  amendment
★  galactus
★  earmark
★  venom
★  ryder
★  masked rider
★  wave precision
★  ruger single six
★  fairfield
★  showa rider
★  wave inspire
★  monmouth
★  inspire
★  ghost rider
★  st peters
★  dukes of hazzard
★  canisius
★  flash rider
★  blackheart
★  deck boat
★  blade
  airwolf
  shane
  uhaul
  sniper
  siena
  concord neo
  dr strange
  black heart
  wave creation
  old high
  rider
  silver surfer
  chatterbox
  power rangers

Your alternative for rider is not listed? Suggest!
Speaking about rider, one probably shouldn't forget about horse.

Other search terms related to rider and their ratings are:
★★★★★ horse
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Google Trends

Scale is based on the average worldwide traffic of rider in all years. Click on graph for more.
rider
addendum
spawn