Hello Basalt,
I don't have any plans for a miniature air compressor, but I can offer some "for whats its worth" comments.
You might be able to adapt a design from a model steam engine or gas engine. The air compressor only has to withstand the heat of compression, so materials for steam or gas will certainly work. Air compressors are all about volumetric efficiency - higher is better. Steel reed valves make it easier to get minimal clearance volume. Design for the smallest clearance volume you can get, and you will still have plenty of clearance left to pass any water droplets. You could also use small ball-check valves. I would go for oil-less design. Use an off-the-shelf sealed ball bearing for the connecting rod/crank pin joint. Likewise, I would use small, sealed ball bearings for the crank shaft bearings. Teflon rings are widely used in compressors these days - even large industrial compressors. This gets you oil-free air without having to worry about lubrication. You might be able to make the entire piston out of Teflon. If the design is belt driven, a flywheel will be necessary to smooth out the crank velocity. You didn't say what type of volume (cfm) you are looking for - that will determine the cylinder dimensions and operating speed. Single stage compression is easy in the 20 - 60 psig range. Single stage compression is possible up to 120 psig or so, above that, two stage compression is usually used to limit the temperature rise of the air per compression. A belted compressor makes it easy to match the motor power to the compressor demand. You can select pulley sizes to keep the compressor from overloading the motor. One problem with piston compressors is being able to start the compressor when under pressure (for example you want to re-start the compressor when the tank pressure has fallen to 30 psig). One solution is to have enough motor torque to do the job. I think this is the best design for a small, model type compressor. Otherwise, there are different schemes for "unloading" the compressor until the crank comes up to speed. For a quick and dirty estimate, lets say you have a 0.5" bore and a 1" stroke at 300 rpm = 60 cu in/min. Say you can get 50% vol eff = 30 cu in per min (measured as intake air). Say you are compressing to 60 psig into a 3" dia x 10" ln long = 200 cu inch tank. 60/15 * 200 = about 800 cu in of free air to fill the tank. At 30 cu in / min = 27 minutes to fill the tank. In reality, it goes a little faster since you are pumping against less than 60 psig for the first part of the cycle. The shaft horsepower required would be around 0.1 hp.
Might give you some idea if this is the scale you are looking for.
Terry S.