Ms. Karla, I certainly encourage you to find a ceremony, perhaps Confederate Memorial Day, to raise a Confederate flag at the cemetery. I have done so on several occassions. It would not be proper flag etiquette to fly a Confederate flag beneath any other flag, just as it would be inappropriate to fly a U.S. flag under another one. After all, they are both American flags.

My suggestion is that you lower the U.S. flag, with proper respect, and raise the Confederate national flag for the duration of the event. Or, if there is another flag pole of equal height, utilize that one.

Rules for Display of the American Flag

Flown on the Same Halyard with Non-Nation Flags
The American Flag should always be at the peak. When the flags are flown from adjacent staffs, the flag of the United States should be hoisted first and lowered last. No such flag or pennant may be placed above the flag of the United States or to the right of the flag of the United States.

http://www.usa-flag-site.org/etiquette-display.shtml