Can I install two thermostats to control one furnace?

You not only would need a second thermostat, you would need a switch to turn one on and the other one off. The wiring would be sort of a nightmare.
Of course if you do not heat the living room, it may get too cold and then warming it up in the morning would probably use up any propane that you saved during the night.
Use an electric blanket and maybe a small electric heater in the bedroom and turn the living room temp down a little bit at night.