Well, after all of those fine words from my accomplished colleagues, here's something you might even be able to use.

I find that a good melody is harder to create than anything else, but the satisfaction is worth it.

One method I use is I start playing random chord progressions until a melody slips out from between the chords and into my ears. What's really happening is that I'm just sort of combining elements of those chords in a new way (which is why so many songs can be played with the same chord progression).

Arlo Gutherie said at Clearwater this year that the key to songwriting is not so much a matter of coming up with original stuff, as it is stealing the existing stuff and disguising it so well that even you can't recognize it. So try playing the exact chord progressions of a song you really love the sound of (such as Greensleeves or Michele or Drop Kick me Jesus through the Goalposts of life or any other melody that you're really in love with) and see if you can start to "hear" a different melody in those same chords.