DC - DC Amplifier for Piezo Buzzer
You could use an inexpensive motor driver chip such as the Diodes ZXBM5210 (plus an inverter, such as 1/6 of a 74HC04 or a MOSFET + a resistor). 

You put the piezo plus a small series resistor- perhaps 50\$\Omega\$- in place of the motor. Internal circuit looks like this: 



So you would switch between Forward and Reverse using your port pin (you need the inverter to feed the complementary signal to (say) Reverse while the Forward input gets fed directly. 

Note that this is a push-pull driver, so the peak-to-peak voltage across the piezo will be a bit less than double the supply voltage, so 9-10V is fine for the supply. 

The resistor is to limit the peak current to 200mA since the piezo looks like a fairly low ESR capacitor. Put a good bypass capacitor on the higher voltage supply (perhaps 220uF/16V electrolytic or at least a 10uF/25V ceramic). 

This chip has built-in dead time of about 3us so you can just drive the inputs in complementary fashion without worry. The PWM input should be tied to Vdd to avoid the chip itself doing PWM. 

I also suggest putting a couple K ohms of series resistance in series with the port pins, just in case something gets shorted to the 10V supply it might save the processor from destruction. 

Chances are the piezo will not fail with much higher voltage than the rated 20V, and this chip is rated for 18V maximum supply (36Vp-p) if you feel lucky and want to try it.