The issue with silver, platinum and diamond is that they are all usually represented with similar colors. Color alone would not be enough, but shape can go a long(er) way. You mention you want your icons to be really small, if that's the case, only way to go is very simple shapes, like Stein mentions. I don't think it would be a good idea to have two elements of practically the same color, so I'd definitely try with a yellow:
There is a website I used to participate in, and it was the first thing I thought of when I read your question. They use a badge system for users reputation, and their badges actually look like medals:
So they play not only with the color and shape, but also the size. I think one of the most important issues here is that any group you chose to use, you need to make visible as a whole. For example, the small medal in the example only makes sense if you have seen the bigger ones at least once (until I saw them, I thought my small bronze medal was amazing!).
I think this applies to all elements, even bronze-silver-gold, they only work as part of an ensemble (a gray circle if you haven't seen what other users have is just a gray circle ad nothing more). In this case, size made sense when users were listed and you could compare the medals.
Now, I started thinking about this problem and if there was any workaround. If color, shape and size are not enough by themselves, and you can consider going a bit bigger with the icons, how about a realistic interpretation? A diamond is easy, everyone knows what they look like (at least in 2d!). The problem comes with platinum and silver, one of them will look a lot like the other. But using realistic illustrations could allow for some freedom, so why not "diamond, ruby, emerald"?
Image source: Iconfinder
Hope it helps!