I would try this first:

https://www.gardenweb.com/discussions/5477475/paint-inside-of-glass-front-cabinets#n=15

I have used it to cover wood closet shelves. I have also used it on the front of a tall file cabinet. The shelves worked out good. The removable contact paper starting to curl a little on the edges of the file cabinet. It could be because it is glossy metal. Try a roll and see what happens.

I would prefer a flat finish and contact paper isn't (as far as I know). So I would go with wallpaper. If you're not comfortable papering the cabinets, then you could cut foam board to fit and paper that. It just pushes into place if cut well...

You can also use sheets of scrapbooking papers (from Hobby Lobby or Michaels), or wrapping paper.

The problem with the china is that it is wide so many of these options would need to be pieced and I wasn't wanting to do that. The china has a dark brown back and we were wanting to do something to lighten it up inside. We are somewhat open to painting it as a last option. Writer, I quickly looked at that thread earlier today but thought they were wanting to paint the glass. Silly me!

I may try it on my bookshelves and see how it works.

Years ago, I covered the back of some plain white bookcases with fabric to coordinate with my son's room. I am now in the process of changing the fabric out for an adult update. I think I used an adhesive, but there are removable options for that. Even watered down Elmer's that would wipe off with water down the road. I would test whatever you are considering to make sure it has enough cling to stay put on a vertical surface but can still be easily removed.

If you go to paint, I'd do poster board so it can be removed down the road.

I have covered a ton of wood and mdf with contact paper. It is about as thin as 3 sheets of paper stacked together but it does not really tear because it is made out of some sort of vinyl or plastic I assume. Not paper. It does not appear thin and it isnt see through, at least not the contact paper that I have used. I think it would work fine for your application.

ETA - This photo shows a ton of 2x4's, mdf, and book shelves covered in cheap contact paper. If you look at the end of the bed, the striped piece is all white melamine bookshelves covered in 3 different colors of contact paper cut into strips. This is what $6 contact paper looks like.

I like the contact paper but I think Penny has a great suggestion with the Rub N Buff also.

Do you have a picture? What about using rub and buff in gold...Or metallic wallpaper?

I just adore what this does to an otherwise (kind of) unnoticed piece..