I had the same problem and here how I figured out a solution,
Assume your stereo jack is connected to the folowing pins;
Pin 9 = Left stereo
Pin 10 = Right stereo
GND = Ground
The solution relies on using arduinos inner circuitry.
Pin 9 and Pin 10 are our pins to control left and right stereo sounds.
We need a third pin which will be the main output source for stereo both(left and right) condition.
Say this pin be Pin8.
Connect Pin8 to Pin9 and Pin10 by two resistors of 1kOhm or similar depending on your sound level choice.
When you seet pin8 mode to OUTPUT, pin 9 and pin 10 modes to INPUT, and when you play a tone at pin8 as tone(pin8,duration,frequency) will play stereo on the headphone.
On the other hand if pin9 is set to OUTPUT and pin10 set to INPUT, playing tone at pin8 will flow the current through right pin of the stereo jack, right sound.
Similarly if pin10 is set to OUTPUT and pin9 is set to INPUT,and tone played at the pin8 send the current through left stereo jack connected to pin9, left sound is played.
Hope this helps.