Leds in series with buzzer without resistor
Putting them all in series should work okay. 

If the buzzer is 3V and 20 mA then it has a resistance of 150 Ω.
The buzzer would act as your 150 Ω current liming resistor. 

I would first power the LEDs with a 150 Ω resistor to see the brightness then use the buzzer in place of the resistor and see if the brightness is about the same. 

The bigger problem I see is the 9V battery.  It will provide 9V for only a short period. Notice below how quickly the battery voltage drops to 8V.  This may not be a problem if the buzzer is not activated for long periods of time and you use a fresh alkaline battery.