how to do an amplitude modulation in Ableton Live
If you have Max4Live (included in Live9 Suite), it should be easy enough to build a Live device that does the amplitude modulation exactly the way you want.

Otherwise, look for Ring Modulator and Amplitude Modulation VST plugins. The easy way to write a Ringmod plugin is to just do amplitude modulation. So the free plugins are likely to do what you want. Actually modeling an analog ring modulator takes more effort, but maybe that is the sound you are really looking for.

If you happen to have Absynth, I'm pretty sure you can accomplish AM or ring modulation on arbitrary incoming signals with that.