Provide a Soft Background
You can still have a fully black curio cabinet without having a black background. Maintain the dark shelves and sides, but put a soft color on the back to ease the boldness a bit. You may think of simply painting it a soft shade of beige, or you may put wallpaper on the back to give it more texture. That part is up to you, but make sure that your dishes will still slightly stand out from the background.
Many curio cabinets already come with lighting built in, but if yours does not, you may think of adding some to the shelves. This will help your dishes stand out, but it will also provide a warm glow from within that will dull the boldness of the black coloring. Bright white lights may not be a good idea, but soft yellow ones should fit in fine with any pieces that you have. If you are going for a more modern look, you could even add colored lighting, given that the dishes fit the theme.
Use Light Dishes
If you put dark dishes in your black curio cabinet, you are only going to add to the heaviness of the piece. Instead, you should add light or metallic pieces in there to balance the dark colors of the shelves and sides. Bright white may be a little much, but a soft eggshell or tan could be the perfect fit for you.
Add Other Black Elements
If you add other pieces of black in the room, the black curio cabinet will not stand out as much. This creates a balance in the space that would make the cabinet fit in, rather than throwing off the look of the place. You do not need another large piece; just a few simple accents here and there should do the trick. You can then proudly display your curio cabinet for what it is.