Consider a C major 7th chord - C, E, G, Bb. Use all the notes of the chord except the root and you have an E dim chord (in sheet music the dim is sometimes indicated with a little circle, like a degree symbol). In practice however most diminished chords have a diminished 7 as well as a diminished 5. So from your original C7 chord, move your C up to a C# and you have a diminished chord which could be described as C# dim, E dim, G dim, or Bb dim depending on its function. If you're going from, say a C to a D minor, you could put a C# dim in between and give yourself a moving bass line off the C chord.

My own feeling is that in Stephen Foster's "Hard Times" (in the key of C, say) there should be a dim chord on the "wea-" as in "song, a sigh of the WEA-ry." Folkies usually simplify to an F chord, try a C dim (or F# dim) and see whether you like the sound. If you do, dust off the row.