when i teach students to write I tell them to start with Lyrics, then Chords, then melody. Of course, in reality all of these are interchangeable and often happen at the same time, BUT, having the chords first, suggests melodies and you are not then stuck in the position you are.
I often have students who sing the melody and then I add the chords, but it is experience that allows you to do this, just knowing what you are listening out for. And of course, there is no right progression, often 4 or 5 can work. It can all be done by ear but I think having some theoretical knowledge allows you to consciously do the unexpected.
anyway, only advice I can offer is to work out the notes of the melody on a piano and look to see what chords may fit...
hope it helps
Chris
www.chrislong.me.uk