I have installed a coal stove next to my oil furnace. I have duct it to the furnace so I can use the fan. I have the fan running all the time but I want to be able to have the thermostat turn it on and off as it requires more heat. The thermostat is programmable
With a fan only setting. But there is only a black and white wire running to it.

If you only have 2 conductors running from the thermostat to the oil furnace you are not going to be able to control just the fan from the thermostat. Evidently the oil furnace controls the fan on a call for heat and the fan won't run unless the burner is firing. You will have to rewire the thermostat with at least 3 conductors. The green one will call the fan. Of course the oil furnace must have provision to wire it that way.