OK, thanks for explaining. what you are trying to do is reverse the action of the relay without drawing any more current than is necessary.
I'm assuming your relay doesn't have an NO contact as well, if it has, swap the buzzer to that instead of the NC contact. With the present system you will still have to energize the relay to keep the NC contacts open and that will also drain your battery. What voltages are you using for the buzzer and the relay coil? This may be a very simple fix using a transistor instead of the relay and if it's suitable it will draw almost no current at all.
Brian.