I think the best result you will have with an DC/DC converter. You can generate a negative supply with a battery of 1.5v por example.
The other option tou have is to use charger pumps, like used in rs232 transcevers and the third option is to use a negative linear voltaje regulator like 7912 with some diodes in the 2 pin, like this regulator have a quiescent current of abaout 4 mA, you will have sufficient current to biassing diodes and they will drop about 0.7 v. I think there are variable negative voltage regulators. like lm317 for positive voltaje. Check National.
I hope you be usefull