Ideally, you keep track of the days he works in GA. You withhold GA tax only on the income he is paid for days he physically works in GA.
When you issue the W-2, you use two lines for boxes 15-20. You show the GA wages in box 16 on one line (with "GA" in box 15) and the GA withholding in box 17. On the 2nd line, TN in box 15 and the TN wages in box 16. The TN box 16 plus the GA box 16 should equal the box 1 amount (federal wages).