I only know of one good song you can play in standard guitar tuning with just 2 fingers: Feelin' Alright by Dave Mason, in the key of E.

Men generally can't even sing it in that key. Joe Cocker's famous version is sung in C. The chorus: "Not feeling too good myself" is not exactly the greatest message.

Here is a free PDF file that is a free chart of all the 2-finger chords in regular tuning. Good luck playing any other songs with these chords. Most of them also require stretching across several strings and frets.

Using Liberty Tuning, you use chords that are actually easier than the E7-A7 chords in Feelin' Alright, and instead of one song you can play millions. (And it's easier to play Feelin' Alright...)