Fun question! I think this is totally do-able.
Horses generally sit or lay on the ground, but ordinary chairs are designed to suspend the booty above ground level with the knees bent in a way which allows a person to easily exit the chair at will. The human buttocks is ideal for resting on, because it is naturally cushioned. However, the underside of a horses belly doesn't have that natural cushioning, and it's hard to imagine a system wherein quadrupeds rest on something with all four of their legs bent and propped in front of them. This makes a direct analogy for horse-chairs difficult, but not impossible.
Here's what I'm thinking:
You have a long bench, at least 3/4 the length of a normal horse, and about the height of the horses knees. It is curved downward to a concavity in the front to accommodate the horse's rib cage, and curved upward to a gentle, parted wedge in the back to comfortably fit between the horses hind legs. The bench is widest in the front near the ribs, and thinnest in the middle, just in front of the hind legs, so that they can be brought forward against the sides of the belly and bend downward at about 90 degrees, straddling the thin part of the bench. The front legs stretch forward in front of the bench and bend down at 90 degrees. It almost looks like a bent spoon.
The bench has four legs. The back legs are simple, supporting the rear of the bench. The front legs turn forward and slightly outward at 90 degrees at the place where they touch the ground. About 2 feet in front of the chair, the legs turn upward and back toward the chair, like this:
front legs (side view): /__|
The frontward appendage of each front leg, at an angle of 45 degrees to the ground, is long. Each frontward appendage of the front legs stretches a few feet above the bench itself before they connect with one another at the top. The place where they connect is a back rest, which is high off of the bench so that it only supports the upper back of the centaur's humanoid torso. This is so that the centaur can duck under it when it mounts the chair.
Moving backwards is uncomfortable for a horse, so when the centaur goes to sit on this chair, it approaches the chair from behind, lowers its human body to go under the back rest, then lays its horse body on the bench, and then raises its human body to lean it backwards against the rest.
The parts of the front legs which rest parallel to the floor are angled slightly outward from the chair itself, making kind of a Y shape if you look down from the top. This is so that when the centaur dismounts the chair, it can just stand up and walk forward. Alternatively, if there is a table in front of the chair, the horse will have to stand, bow its human body forward, and step backwards to go under the back-rest again.
If you wanted to get more complicated, you could have like a guillotine system where the backrest comes down behind the torso from above, so that the centaur didn't have to bend over so much.
I hope this helps!