Howard's suggestion of taking a known tune then tweaking it is what I call "chop-shop songwriting". You file off the serial numbers, change the body lines, give it a new coat of paint, and voila! a new song. (Is it coincidence that the theme from the movie "Star Wars" is awfully similar to the theme from the movie "Born Free", except turned upside-down so where the pitch on one goes up, the pitch on the other goes down? Or tweak the rhythm of "Spancil Hill" and you get pretty close to "Gilligan's Island")
This has the advantage of taking a "good" melody (one that you like) and hopefully preserving the elements of rhythm, pitch relations, etc. which make it "good", without having to have a detailed understanding (intellectual or emotional) of those elements. It's a useful shortcut in the craft of songwriting.
It has been said that all tunes are related to some other tune - after all, there are only so many notes, and a finite (if very large) number of ways to arrange them. Very few songwriters can truly say they were not in any way influenced by other tunes they have heard. The trick, though, is to be inspired by those influences but be careful about directly copying them - at least not too much.
Another option, if you play an accompaniment instrument: find a chord progression you like. You already have a sense of the rhythm you want. Start playing the chords & reciting the lyric, and then just decide which note in the chord you want to sing.
Good luck in wooing your muse!