-9V from +12V - Available Options
There are many, many chips that you can utilize for this function. The simplest topology is probably inverting buck-boost, but there are others. Here is one of the cheapest and oldest chips (MC34063) in the inverting buck-boost configuration:



Obviously you would change R2/R1 ratio to get the correct -9V output voltage, as well as Rsc, L. The output capacitor could be reduced. You can go through the detailed design procedure in the datasheet. There are also some online calculators but I can't vouch for their accuracy. 

Because the chip is old (low switching frequency) and your current low the inductor L will turn out to have a fairly high value, probably between 300uH and 1mH.