so...appoint her leader of the demon army, and, if she balks at first, just point out that as she is conquering the world she might find someone who can kill her AND that if that fails then once she has actually conquered the world she can command everyone to search for a way for her to die
pros:
as has been pointed out she might lose her immortality for turning against humanity
if not, either she leads the demon armies to conquer the world or dies trying, either way you profit in the end
once she does die, the demon armies will have notable progress towards world domination if it hasn't been completed already
you don't really have to do anything and she'll *probably* stop visiting you every day in the hopes you can kill her
cons:
eventually something's gonna show up that can kill her and you might have to deal with that afterwards, but at least it wont be in her immortal hands
...possibly after everything has been tried nothing can kill her and if that is the case then one by one she'll probably kill everyone for failing