7809 Linear Voltage Regulator Outputs in Series
It should work. Spreading the heat dissipation between two regulators may make things easier. 

You may wish to put an inverse-parallel diode across each of the 9V outputs that you are going to series. The reason is that if you consider what happens when the output is short-circuited - there will be two regulators each trying to drive the other one negative and one will win. That may harm the regulator that's driven minus and it also could harm the output capacitors (if they're polarized types). Something like a 1N5403 would work fine.