Of course it's possible, but it's not simple. At the most basic level, it would require an oscillator.
Since all voltages are relative, you could easily put two identical resistors in series between your two supply terminals, and call the middle connection "0", and the other two connections "+4.5" and "-4.5". You can increase the absolute voltage difference using capacitors and step-up circuits.
The short, practical answer is to use the +9V as a power supply to a pulse-generating microcontroller or IC, and also as a power supply to some amplifiers which change it's output to whatever voltages you need.