Cook is one of two Georgia inmates scheduled for execution this week. Warren Lee Hill's execution was put on hold Tuesday, less than an hour before he was to die by lethal injection.
Cook and Hill argue the state is violating the law by using pentobarbital in executions without a prescription.
On Wednesday, the state asked the court to deny Cook's request for a stay and lift the stay it granted for Hill. The state argues the challenge is frivolous.
Earlier, the U.S. Supreme Court denied Cook's request for a delay and the state Board of Pardons and Parole denied his clemency request.
Cook was convicted of killing two Mercer University students in 1995.
http://accesswdun.com/article/2013/2/258530