Barring access to real wooden wheels and the axle to support them, may I suggest you build a small platform (maybe 2 feet wide by 3 feet long and approximately 18 inches tall) with casters underneath (swivel in the front and fixed in the back - 3 or 4 inches in diameter) that can be built up to fit under the base of your chariot.  Make this platform smaller across than the base of your chariot and paint it flat black.  (Rule NUMBER ONE in community theatre is if you paint it flat black it becomes invisible.  Yeah, I know, bad joke!)  I'm suggesting a PLATFORM with FOUR casters because it would be far more stable than a simple frame and only TWO casters underneath.  Next, create the body of the chariot with bent wood railing (or pipe would work) and 2 by 3's.  Skin the exterior surface with 1/8th inch paneling (smooth side out) or any bendable, thin material (maybe rope or fabric?).  Next put a length of 1 inch conduit though the platform, just under the base and position a couple of 36 inch decorative wooden wheels from Harbor Freight Tools on either side, making sure the wheels just touch the floor, but don't bear any weight.  These wheels, while cheap, are for looks, not function.  You can "build them up" with papier mache or something added to the spokes if they need to look heftier.  If the wheels just touch the floor and can turn freely on their axle, they will turn as the chariot is pulled across the stage.  Add the tongue assembly on the front, attaching it along the bottom or sides of the frame and you're done.  If you want to hide the platform the chariot rides on, you might have gold fabric and/or tassels drape down the exterior of the body, almost to the floor, or something equally deceptive.

By the way, to save room in the wings, the original off-broadway production flew it up out of the way the whole time it's not used.  We produced the show and have no fly system, but we rigged pulleys to do the same thing.