How can I blow a stream of air for up to two minutes at a time?
I think whether the official pneumatics parts would work for this project would depend on how much force and pressure is required to sound the particular harmonica that you are considering. I did find someone who has figured out what the pumps are capable of producing however I can't seem to find a reference for what the tubing systems are capable of supporting.

As a previous answer mentioned, an LA would be unlikely to be able to change notes fast enough so it would be much simpler to put a tubing endpoint at each one of the holes and then control which are active using switches and toggles. However if you do plan on powering multiple end points (which I understand is pretty common in typical harmonica playing) you'll have to think about whether you'll be able to supply enough pressure for all of the notes at the same time or not, and may require multiple compressors.

I would think that the design would end up being something like an M motor based compressor connected to one or more air tanks feeding a manifold with enough outputs for each harmonica hole and then adding a switch inline on each of those outputs.