There are different versions, tempos, etc. for this song. The C7 (I guess that's what you'd call it) is played in same formation as B7 (first position), but one fret up. You could also play it in A7 formation on the fifth fret.

One Meatball (Josh White/Dave Van Ronk combined version)
INTRO (2x)
Em D C7 B7

A [Em]little man walked [B7]up and down,
To find an eating [Em]place in town,
He read the [Em7]menu [A]through and through,
To [B7]see what fifteen cents could do.

    [Em]One meat-[D]ball, [C7] [B7]
    [Em]one meat-[D]ball, [C7] [B7]
    [Em]He could afford but [B7]one meat-[Em]ball. [D] [C7] [B7]