Chun-tzu said:
I always assumed the penalty comes from the speed the mount's moving at. A Centaur that's galloping at full speed should have the same penalties as a guy on a horse galloping at full speed.
Shot on the Run [General]
Prerequisites: Point Blank Shot, Dex 13+, Dodge, Mobility.
Benefit: When using the attack action with a ranged weapon, the character can move both before and after the attack, provided that the character's total distance moved is not greater than the character's speed.
A Centaur is a character with 4 legs and two arms...he isnt a horse and a horseman in one.
All the riding charms operate on the basis of a rider who needs to control his/her mount...I dont think a centaur has the problem of sorting out his own legs when running.
Ergo...the usual feats are enough mostly.
Personally I wouldnt let a Centaur use spirited Charge or Trample, orelse I would give the spirited charge feat to a character charging with a spear as well (and there already is a charge option)...same goes for trample...why shouldnt a half orc be able to trample on a dwarf.
Thats just my 2 cents.