I have an older oil furnace and an older non-programmable thermostat with a mercury bubble in it. Only two wires: beige (white?) and black. Can I install a programmable thermostat? All the models I've seen seem designed for four, five or more wires.

A programmable stat that uses batteries. i.e. doesn't need the (C) wire hooked up.

Make sure it can be configured for a "conventional furnace" (oil, gas) or electric.

Then use (R) and (W)

Wish you were close to me. I have a cheap Hunter programmable laying on my parts shelf that I would like to be rid of. I don't like them, but it would work for this application.