C, G, G, C...F, C, G, C ought to do it. I will take the liberty of adding that a good 80% of Western folk songs can be happily peformed by mastering three or four chords in the key of your choice. These chords, traditionally, in the order of frequency of use, are the tonic, the subdominant, the dominant, and the relative minor.
Counting on the major scale the tonic is the first note (the one the key is named after). The subdominant is the fourth note of the scale (in the key of C, the subdominant is F) and the dominant is the fifth note of the scale. (In C, the dominant is G).
If you learn these three chords -- C, F and G -- you will be able to play a huge number of songs. If you add the relative minor, which is A minor in the key of C (the sixth note of the scale, but made minor), you can do another huge number of songs including "Oh, Donna" and "Teenager in Love", should you wish to.
In the key of G, the same triad is G, C and D. The relative minor is Em. Just for another example.
Work the song against these chords, and you will find you can work out a very large numbe rof them for yourself just knowing this much. Add the second (such as D in the key of C) to use when bridging from (for example) C to G and you have another whole collection.
You will get a lot further singing and playing if you use these basics to work out accompaniments than you will seeking rote chord sequences to stick to, one song at a time.
Given enough fooling around with these sequences and you will be able to play by ear a large per centage of the time.