Open your soundtrack in the software program. At the top of the program, choose "Send To" and then "Soundtrack Pro Audio File Project." This will open the file in an audio waveform format.
While listening to the soundtrack, drag across the waveform during the cough that you want to remove. Do not drag across any sound that you want to keep. This might take a few tries so that you don't accidentally delete any sound other than the cough.
Up at the top of the software, find "Noise Reduction" and choose "Noise Print" to set a noise print. This will store the unwanted sound in a separate clipboard.
Drag across the cough that you want to remove again, and this time choose "Reduce Noise" under the "Noise Reduction" tab. This will open a display box that allows you to tune the settings around this noise.
Slowly drag the "Noise Threshold" slider to the right until the cough is gone. This will also cause the speaker's voice to become robotic. After the noise is gone, drag the "Reduction" slider to the left to return the speaker's voice to normal.
Move around the treble and bass to cover up any part of the cough that you were not able to fully remove. Increasing the bass will make the voice sound warm, while increasing the treble will cause the voice to sound clear and concise.
Click "OK" once you are happy with the way the clip sounds. Play the song over again and make sure it sounds the way you want it to before clicking "Save."