Sound synthesis effects for natural sounds
First, grab Sonic Visualizer, it is much better than Audacity for looking at sounds.

What you see here is probably the result of the sum of two simple and stationary sounds at fundamental frequencies close to each other. This causes beating of their fundamental, causing the amplitude modulation (tremolo) you observe.

Two important factors make a synthetic sound "feel" natural:


Whether it accurately reproduce the sound of the original instrument over time. Some criteria to look at: timbre (distribution of harmonics), timbre modulations over time, amplitude modulation over time (presence of tremolo, overall amplitude envelope), pitch modulations (presence of vibrato, does the instrument instantly reaches the target note or is there a short transition like on brass instruments...).
How it responds to control by the performer. You have to list which parameters, along with note data, will be available to your system (will it synthesize sounds from a bare MIDI file? From a MIDI keyboard sensitive to velocity and aftertouch? From a dedicated hardware device emulating an accordion, with accelerometers and pressure sensors?), and understand how to map these inputs to synthesis parameters. You also have to list which controls the performer will have over the system (for example, is there an option for the user to switch on/off the different registers?).


I will mention 3 synthesis approaches you can follow for this problem:


Sampling. Record, one by one, all the notes of an accordion, under different performance parameters (how hard the below is moved for example, all different combinations of registers). Play back from this exhaustive database of sounds, with loops to make them last as long as you want. Advantages: a note taken in isolation sounds indistinguishable from the real thing. Drawbacks: might sound "fake", and will not respond to performer input (not "expressive") unless you start doing some signal manipulation on the recorded sample - at which point they won't sound as natural as they were recorded. A lot of disk/memory used by the samples. Warning: it's quite an involved job to exhaustively sample an instrument and organize all the data, and there are already companies very good at doing this kind of stuff - it'll be hard to beat them.
Classic subtractive synthesis. You could start with two square or pulse waves, slightly detuned to get beating, a tad of high-pass filtering to give it a "nasal" quality, and an EQ to color this... Then stack several of those to get different registers. Check in the patch libraries of classic "old" synths (JX8p, D50, M1)... they all have decent accordion sounds which are totally sample-free. Advantages: can be made very expressive - since you have control over the whole production of the sound, you can easily map input parameters on sound parameters. You won't have to reinvent the wheel and can base yourself on existing sound synthesis code. Inconvenient: will sound "synthetic" (but "lively &amp; synthetic" is sometimes better than "realistic &amp; dead"!).
Physical modeling. You could get something more realistic than vanilla subtractive synthesis by using physical modeling - try cobbling together (for example in csound, Max/MSP or supercollider) a few reed models (the 3 mentioned programs have basic primitive for physical modeling - but I'm not sure they have free reeds), add EQ or a simple resonator. Ideally, you could get something both realistic sounding and controllable, though it's not the easiest path!