Various options depending on stuff like, is perfume container pressurized expulsion or manual push button/pump expulsion? How long must it spray for?
For a pressurized container a servo armature may be enough to depress button or maybe a cam on the end of a geared motor/stepper shaft. For manual atomizers maybe a solenoid or peristaltic pump.
A piezo disc will work as an atomizer; that's the technique that some battery powered air fresheners use. As another option it might be possible to hack an old inkjet cartridge to do the spraying. Or like Riva's idea with the old-fashioned atomizers you could just use a servo to push on the bulb/nozzle.