Character Controller for quadruped character

Unfortunately, the CharacterController is always an upright capsule collider - you can't replace it with a box collider or horizontal capsule, nor add other colliders to it: the CharacterController "thinks" that it's colliding with the other colliders, and stands still or moves to stupid directions.
The best you can do with a CharacterController is to adjust its height and radius so that it becomes a sphere (radius = height/2). If this doesn't work fine in your case, a possible solution is to use a Rigdbody character: try a box collider with the wiki script RigidbodyFPSWalker - this script requires a capsule collider, but you can remove this restriction like below:

 var speed = 10.0;
 var gravity = 10.0;
 var maxVelocityChange = 10.0;
 var canJump = true;
 var jumpHeight = 2.0;
 private var grounded = false;

 // capsule collider removed from this line:
 @script RequireComponent(Rigidbody)
  
 function Awake ()
 {
     rigidbody.freezeRotation = true;
     rigidbody.useGravity = false;
 }
  
 function FixedUpdate ()
 {
     if (grounded)
     {
         // Calculate how fast we should be moving
         var targetVelocity = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));
         targetVelocity = transform.TransformDirection(targetVelocity);
         targetVelocity *= speed;
  
         // Apply a force that attempts to reach our target velocity
         var velocity = rigidbody.velocity;
         var velocityChange = (targetVelocity - velocity);
         velocityChange.x = Mathf.Clamp(velocityChange.x, -maxVelocityChange, maxVelocityChange);
         velocityChange.z = Mathf.Clamp(velocityChange.z, -maxVelocityChange, maxVelocityChange);
         velocityChange.y = 0;
         rigidbody.AddForce(velocityChange, ForceMode.VelocityChange);
  
         // Jump
         if (canJump && Input.GetButton("Jump"))
         {
             rigidbody.velocity = Vector3(velocity.x, CalculateJumpVerticalSpeed(), velocity.z);
         }
     }
  
     // We apply gravity manually for more tuning control
     rigidbody.AddForce(Vector3 (0, -gravity * rigidbody.mass, 0));
  
     grounded = false;
 }
  
 function OnCollisionStay ()
 {
     grounded = true;    
 }
  
 function CalculateJumpVerticalSpeed ()
 {
     // From the jump height and gravity we deduce the upwards speed 
     // for the character to reach at the apex.
     return Mathf.Sqrt(2 * jumpHeight * gravity);
 }