I alway bought my POH copies from the FBO where I was flying the airplane in question. That way, I had a good chance of getting the POH that was closely associated with the actual plane I was about to fly.
Reference, we had four different models of 172 on my old ramp, so getting the correct POH was importrant.
I doubt if any are in public domain. If any are avaiable they are probably on a manufactures website for a fee. The most common training aircraft POHs may be available from some pilot catalogues. I believe there is a point (maybe 1979) where the term POH became Aircraft Flight Manual. A POH usually is a generic operating book legal for a whole series of aircraft (ie PA-28-181) and an AFM is issued for a particular serial number aircraft. If you are using it to replace the book kept with the aircraft, check into this. If for study purposes, don't worry about it.
Here is the "library" page for a local airport FBO. There is no restricted access to this page, it is open to the public. Although under new management, it is the field where I learned to fly. Just click on the appropriate places. Enjoy.
I'm not 100% sure this is correct, but at the FBO's I trained at they always had POH's on the aircraft they rented they could be purchased. I remember that someone told me to be sure not to use these POH during check rides with the FAA. We had to get the original poh for that plane on checkrides.
Again, don't know if this is true, just what I was told to do back then.
The FAA will only want to see you making reference to the AFM, the Airplane Flight Manual. It is a "special" version of the POH that applies to an individual airplane. The two books may be 99.9% identical, but that is of no concern. There is only ONE AFM for an airplane.
Timebuilder - great site from N47. I think if more FBO's/flight schools took the time to put this kind of info together for their airport, there would be less complaining about a lack of business and activity.