This is another one of those named recipes that depend on where you are and how your family makes it. Country beans where I come from are snapped fresh green beans, some salt, water and preferably chopped salt pork or raw bacon if you are out of salt pork, then simmered for at least an hour, usually several.
I remember my mother getting up really early, starting the beans for an hour or 2, while she'd make something else or 2, then we'd make the hour or so drive to my grandparent's home, where the pot would go back on the stove until it was time to eat. She'd make them in the pressure cooker, though didn’t pressure cook, just so she could put the top on the pot and it wouldn't leak if it tipped some on the car trip.
I do like the idea of adding some potatoes and will do that next time I get the urge for country beans.
Thanks!