Either tunes or songs would work in this context. I agree with 马先生 that a song doesn't have to have lyrics. Many songs use only a limited number of chords. For example: http://www.guitarlessons.com/guitar-lessons/guitar-lessons-for-beginners/play-10-songs-with-4-chords/

The short answer is, a tune is a melody and a song is complete. You can't play a tune with four chords, but you can play a tune with four notes. If you have four chords, you can sing any tune that fits them (see my comment of 马先生's answer).

Firstly, a song doesn't need lyrics. "tune" often refers to the most memorable part of a song (the melody, no voice). You can use "tune" in place of "song" in some occasions - particularly songs that are repetitive like dance music, but usually a tune alone does not make a song. I don't know much about music, but I guess you can't make a whole song with only four chords.

One additional point to consider: when referring to a whole "song" as a "tune", it's a bit casual. You might say to your friends, "Let's play some tunes!" and mean "songs" . Outside of casual usage, to me, a "tune" is more the melody of a "song" than the "song" as a whole. A "tune" might be repeated multiple times within a "song". In your usage, about songs/tunes that can be played with a number of chords, since you are taking about the structure of the music, I'd see "song" and "tune" as different in the way I suggested. So either could be right, depending on what you mean.