Timmons Park - This a good one although it was recently re-routed and is a bit confusing toward the end.
Here are a couple more I found on-line that I'm not familiar with.
I'd love for people to chime in and offer others they know of, both in Greenville County and in the surrounding counties.
Update: Hat tip to Otis for the following resource. Upstate Disc Golf Courses
Update: Hat tip to Otis for the following resource. Upstate Disc Golf Courses