Mr. Davis has been on death row for 15 years for the fatal shooting of an off-duty police officer in 1989.
His attorneys have filed numerous appeals, pointing out that several witnesses who originally testified against Mr. Davis, 38, have since reversed their statements and said they were pressured to point the blame at Mr. Davis.
The U.S. Supreme Court recently rejected a request to review the case.
Mark Allen MacPhail was shot while trying to break up a fight at a Greyhound bus station in Savannah.
The 27-year-old father of two had been working in a private security job.
Two years later, a jury convicted Mr. Davis for the slaying.
The Georgia Board of Pardons and Paroles will hold a clemency hearing Monday, the day before Mr. Davis is scheduled to die by lethal injection.
"If the board looks this case with fresh eyes, its members will see the complete absence of physical evidence and the now recanted testimony that was the basis for Mr. Davis' conviction," Larry Cox, the executive director of Amnesty International USA, said during a press conference outside the state board offices.
"Our intent is not to add to the terrible pain that was so cruelly inflicted upon the MacPhail family years ago. As a human rights organization, we cannot ignore one injustice as we highlight another."
Mr. MacPhail's widow, Joan, recently told the Savannah Morning News she plans to attend the clemency hearing.
She said she supported the death-penalty sentence at the trial.
An "extraordinary motion" for a new trial also is pending in Chatham County Superior Court, but Mr. Davis' attorneys said they are placing most of their hopes for a last-minute stay with the clemency board.
"The parole board is the failsafe," said Mr. Davis' lawyer, Jason Ewart.
Reach Vicky Eckenrode at (678) 977-4601 or firstname.lastname@example.org.