Vrftsjtryk

Let's be using your typical centaur: half man, half horse. Due to the nature of their legs, they can't ride animals in the way that humans do. Horse legs just aren't really made to do that.

My question is, what kind of animal could I use or create for them to be able to ride, and how would they mount and ride it?

It has to be at least semi-comfortable for the taurs, and be able to carry a heavy load over long distances.

EDIT: The technology in this world is pretty much dark ages technology.

Use Chariots

Others have suggested carts but I will go one step further and suggest chariots. Chariots only have two wheels so they can handle terrain that carts can't. They can be designed to fit just one centaur (with a cart, the centaur(s) would be knocked around a lot) and have firm railings to grab on it (like the ones made for humans have). Or they could fit 2+ centaurs and/or baggage.

They can be pulled by one or two (some pictures I'm seeing show up to 4) horses, other centaurs, oxen, etc. It makes perfect sense to me that even someone who is strong and healthy and built for speed and distance would need a break from traveling, or might need technology to help out for a great journey.

Since we're considering centaurs I feel free to invent a creature.

1. Let's start with this charming little guy. I give you... the Texas Horned Lizard (Source).

2. 
   

   Lizards can really haul the mail. They're sleek, fast, good jumpers, and notice almost everything around them. That charming little tyke is a bit small for our purposes, so let's modify him a bit.

   
   
   
   
   
   • He needs to be the better part of 7 meters nose-to-tail.
   
   
   • He needs to carry a bit of weight — 675 Kg worth of centaur plus whatever is reasonable for them to carry with them. Let's give him two extra feet (6 legs).
   
   
   • His broad back is a great starting point, but let's provide a bit of an evolutionary convenience. Rather than one spine down the middle, let's give him two spines for strength and flexibility. The result is a hammock in the center of the back that's just right for a centaur to lie down in.
   
   
   
   

And if you really want to amp this up a bit, give him a Frilled Lizard's neck flap. It not only scares the crap out of people, but it provides remarkable protection for the centaur (if a bit of visibility hindrance). (Source) Remember, 7 meters long, six legs, that flap would be reasonably naturally armored.

I definitely wouldn't want to be the fool facing squad of these beauties.

The sheer weight of a centaur's body would make travelling 'piggy back' for any appreciable distance very uncomfortable.

I suggest a specially-designed sling with leg holes to support the passenger. They could then be supported between two draft horse.

1. High-status ones have centaur servants (or horses). Of course they are capable of walking themselves (apart from during sickness or old age)

The carriers work one at each 'corner'.

2. A horse and carriage would work well - again with a specially designed sling.

Bigger horses

Might seem glib, but it’s the best I’ve got. If your centaurs are relatively small then straddling the back of a large breed (A shire horse of some kind, or a Clydesdale ) that is bred for carrying large loads with. Out. Stopping. Is probably your best bet. They’re relatively simple to mount if you have some wooden blocks and can be ridden much as a human rides a jet ski (knees tucked up at the sides) to keep the weight distributed nearer their hips and shoulders. As far as speed over distance goes they can plod away for ages without needing to stop. They were bred for it, after all.

Presumably your half-horse horse breeders will be even better at breeding for big, strong, fast horses, eventually getting back to something more like medieval era warhorse breeds.

Just hope they can get over the weirdness...

How about Elaphas maximus, Loxodonta africana, or Loxodonta cyclotis?

The centaur could ride up an adjustable ramp to the back of the Elaphus or Loxodonta and then stand or line down on the back. Or the Elaphus or Loxodonta could get down on all four knees with its stomach on the ground and the centaur could climb onto the back before the Elaphus or Loxondonta stood up.