How to make a simple negative power supply
You could try using a MAX1044/ICL7660.

This is a DC-DC converter I use for bipolar PSUs in audio circuits sometimes. You can use a 9V wall wart or battery to get a -9V output for example. Just make sure to filter it enough and connect the "Boost" if you're working with audio frequencies. The boost will bring the switching frequency above the audio band so you don't hear that noise.

There are some example schematics in the datasheet you might find useful. I often use the one from Figure 6 on page 8.

Hope this helps!