As with the accompanied or unaccompanied thread, I find myself in complete agreement with Scrump. (You can always tell an intelligent and well informed person - they have the same views as yourself.)

Surely the trick is to start singing the song to yourself in the chosen key, playing the basic chord (e.g. D) at the same time. Quite quickl it will be obvious that a change of chord is needed and it will (almost) always be (in D) G, A (or A7) or Bm that fits. It's trial and error - and that might include 'training' one's ear - but it will eventually work out. I certainly found it difficult when I was a young skiffler! Now it's easy(ish)