All of the below solutions will alter the pitch of your audio (along with the playback speed). To correct the pitch of your audio after the playback speed has been changed you'll need to use a 3rd party audio library (such as SoundTouch, which has an LGPL license, so you can use it in your app, without making it open-source). There is an audio unit (AUPitch), that can change the pitch of your audio, but it's not available for iPhone; only for Mac.
All of the solutions below are tested, and work...
Solution #1 [Best solution]
3D Mixer Unit: Instead of a Multichannel Mixer unit use a 3D Mixer unit and set the k3DMixerParam_PlaybackRate on the input scope.
Advantages: k3DMixerParam_PlaybackRate can be set real-time, while you are playing audio, without any clipping sounds or other side effects. It's also easy to implement once you have audio units going.
Disadvantages: Affects the pitch of your audio, but the difference in pitch is not really noticeable if you only need to alter the playback rate by +/- 8%.
Solution #2
Changing sample rate: Change the sample rate on the output bus of the mixer unit. Changing the sample rate works very similarly to adding and removing samples.
Advantages: Works well if you want to multiply the playback speed by a fraction of an integer (1.2x for example).
Disadvantages: Changing the sample rate of the mixer output can't be set on the fly; only when initializing the mixer unit. Affects the pitch of your audio, but the difference in pitch is not really noticeable if you only need to alter the playback rate by +/- 8%.
audioDescriptionMixerOutput.mSampleRate = 1.2*kGraphSampleRate;
Solution #3
Add/remove samples: Only pass every second, third, ... audio sample to the input of your audio unit (mixer unit in my case) in your render callback function.
Advantages: Works well if you want to speed up or slow down your audio playback by 2x, 3x, 4x, etc. It's also easy to implement.
Disadvantages: You can only multiply the playback speed by an integer factor. Speeding up audio playback by 1.2x for example is not possible by adding or removing samples. Affects the pitch of your audio.