How to receive faint AM light
A telescope (large as possible) followed by a photomultiplier. That will give you all the gain you can handle: you will be able to pick up single photons.

Now you have a different problem: ambient light. You want to not recieve this. This is what signal/noise ratio of the channel means in your context. Amplitude modulation will very much limit what you can do to improve this. Note that a continuous light seen at a distance will waver slightly in heat haze.

If you're trying to do this in the daytime, your range will be greatly limited. At night with a large LED lantern or multiple-watt CREE light and a small astronomical telescope you could probably get decent results with digital audio over several kilometers. You could also improve results with a laser as a transmitter, even a 5mw pointer, although you then have to align both ends rather than just one while avoiding looking down the telescope with the naked eye.