Ok, since it is a cassette style hub, there likely would be an adjustable cone on the non-driveside. Since you mention the bearing cover seems to be missing something in the center, it seems pretty safe to say you are missing a cone. It might be theoretically possible that a bike shop could have a replacement cone, but it would be very difficult to figure out the correct one without having the old cone for comparison, unless it is identical to the driveside cone. With cassette hubs on multi-speed bikes, the two cones are usually different.
The forum requires you to have 10 posts to post pictures, but in the mean time you can upload pictures to an album on your profile.