There are a few different ways you can go about hunting. You can pick a sunny day and just walk around looking on the surface and hope there is something all the other diggers missed. I would wait until just after they've tilled the soil over for this method.
You can also dry screen for diamonds. The diamonds will come out of the dirt clean due to the nature of their structure. Dirt just does not stick to them well.
The final method is to screen in water. There are several places through out the park where you can do this and there are a few different types of screens you can use. The screens below are the ones I have. The round one is called a Saruca, which is what is commonly used in Africa. The other ones are a pair of boxed screens with varying mesh sizes to as to filter gravel. I got my screens from a gift shop at the nearby campgrounds that I was staying at. But they could easily be made at home for just a few pennies. I don't care to pay a little extra if it means I'm supporting a tourist industry.
The method to use each type is slightly different. The Saruca is generally concave in shape so that the heavier diamonds settle to the center during the sifting process. When you place the material into the saruca you hold it just under the water and shake it up and down while slightly turning the screen in your hands. The circular motion will insure that all the heavy materials move towards the center if the screen. When you're done and all the clay is cleaned out with only gravel remaining. Find a clean flat spot and in a smooth quick motion flip the saruca upside down onto what ever surface. Do not do it from too high above the surface because you don't want all your stuff to fall out every where. You just want to lay it out on the table. The reason for this is because the diamonds are at the very bottom in the center. Once you flip it over they're on top and will show up once the gravel dries out.
These screens are a little more straight forward in their use. The basic method is to dump the material into the top screen with the bigger mesh. Break up all the clay and dirt so that it falls through to the smaller meshed screen. Once all the gravel in the top screen is clean set it aside while you work on the smaller screen. By this time it should be somewhat dry enough to pick through.
What to look for.
A diamond in the rough looks like a smooth translucent rock. It has no specific shape like many other gemstones and so it can be any thing. You can look into them but cannot see through them and they feel waxy to the touch. If you find something you think may be a diamond take it to the main building and they will identify it. I have heard, however, that if you find something big the park services will watch where you go back to dig and then call their families to come and claim that spot and force you out, so hold onto your finds until you're ready to leave. For this reason a lot of the fulltimers there never report diamonds that they find. so there are a lot more going out of the park than the park states. Don't let any one else claim a spot you worked hard to find.
While you're in the area you can stay at one of the hotels in town or if you go past the park from Murfreesboro about a half mile down the road you will find a pay-to-camp campground. The rates there are fairly reasonable and they offer free wifi, a shower room, a gift shop as well as a large collection of rocks for sale. I would definitely check it out. Before heading out though, check the weather. When I went they had the biggest rain storm in 20 years which lasted for five whole days. So unfortunately I never found anything, but there is always next time.