You would need to check with your specific dates, times, location preference, car size,
etc. for prices. I can't do any specific checking for you regarding a one way rental from Atlanta, but I can give you some basic tips!
1. Comparison shopping.
Find location information for as many car rental companies as possible in Atlanta to check availability and rates. (Try individual rental company websites or do a rental car search on YellowPages.com). Also check multiple locations within the same city (Atlanta airport vs Atlanta neighborhood location, if that is something that you are able to do), for the city, pick up and return dates and times and the car size or vehicle size that you're looking for. Sometimes an off-airport location in Atlanta will have cheaper rates, but they also usually have less cars than airport locations -- that can make getting the availability for a one way rental from Atlanta more difficult. Also, make sure that your preferred company has a drop off location in Charleston, as well.
Check one way rental from Atlanta rates using a discount code, if you qualify.
2. Use a Small Car
You'll want to make sure that the vehicle is still comfortable for extended driving periods, but the smaller the vehicle, the more fuel efficient it will be -- saving you money on gas. But also compare other size vehicles as well; sometimes, smallest isn't always the cheapest (but keep those gas costs in mind!)
3. Timing is Key
The rates for a one-way car rental are often higher for each rental day. (Although some companies do charge a regular per day rate and then add on a one way car rental drop off fee). Usually, the sooner you drop off the car in Atlanta, the less days, the cheaper the rate, IF the company is charging a higher daily rate and not just a flat drop off fee.
Make sure to check which way your car rental company charges for the one way rental that you'll be picking up in Atlanta. If you need a car while in Charleston, South Carolina it will usually be cheaper to rent a separate vehicle for the remainder of your rental period.