Yes, "Farewell to Tarwathie" is a two chord song in the above format. It was the first one I learned to play on the guitar, with A and D chords. I've since transposed it to E and A, as it is in Rise up Singing: A and D is a little high for my voice.

I sometimes also play "Masters of War," this way, with Em and Am, although one should really have a D in there.