In my experience, King, if you want to write traditional music, then you listen to, sing and play a lot of traditional music. Expose your brain and fingers to lots of it.

If you don't want pop sounds, then don't listen to pop. The brain is molded by what comes into it, whether we like it or not.

If you know music theory, it will help to analyze good traditional tunes.   

Then, when you see a set of good lyrics, relax and let your brain 'send ' you the melody. You can't force good melodies, they have to well up.

For example, on my computer I have a little collection of tunes that were in my head when I woke up in the morning. I have to record them before breakfast, or they will be lost forever. I also find that tunes can well up when I'm washing dishes or driving a car in a relaxed setting. Have a little recorder ready, or they will disappear forever.

Frederic Lowe, who wrote the music for 'My Fair Lady', got his melodies to come by driving for miles around pretty Connecticut countryside.