Sorry, you can’t. AVAudioPlayer does not provide any mechanism for precise control of the start time. The currentTime property sets a point in the file for reading, this does not guarantee that the AVAudioPlayer instance will start playing at system time, which is what you need to synchronize several audio streams.
When I need this behavior, I use RemoteIO Audio Unit + 3D Mixer Audio Unit + ExtAudioFile.
EDIT
Note that with iOS 4 you can sync multiple instances of AVAudioPlayer using playAtTime:
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