If you want diamond hoop earings for under $200 you'll have to go with a small pair or a pair that only has a few diamonds, if you want the diamonds to be real. You can get them at any jewelery store.
You can probably find diamond earrings online, or even just in walmart or kmart. If you want to make sure it is real and not a knock off, you can go to your local jeweler and see what they have for under $200.
I think you can travel for countrys which had gold mines and look for one. But the travel will be more expensive than the ring.
Maybe if you can buy an used ring or buy from internet, you can find a good price.