The Apache trail isn't as rough as people think. It's a well maintained state highway, just gravel. You could technically take any sedan up there you wanted, although a SUV or Jeep is best.
I think there are some off-road outfitters if you're looking specifically for a Jeep, although, like I said, any car, truck, or SUV will work (in fact, I'd say shorter is better), I can't think of any names since I haven't used any, but I can check.
-Brad