Melodies are shapes painted by musical notes. A melody line goes up, then down, then up again, and its particular shape helps make it unique and interesting.
Ordinary, everyday speech has its own shapes. Even without musical notes, the pitch of a person's voice moves up and down in the course of an ordinary sentence. Some of these pitch movements are universal expressions, some are characteristic of a specific language or region, some express specific emotions, and some reveal the speaker's unique personality. Use your songwriter ears to listen to the shifting pitches of everyday speech, and you'll find music everywhere you go.
When you have a new song lyric to set to music, try saying the words out loud in as natural a way as you can. Imagine that you're actually talking to someone, using the words of the song, and it's important that they understand what you're trying to say. Notice the pitch of your voice as you say the words. (If it helps, record yourself speaking, and listen to the playback.)
Often you'll hear three pitches in your speaking voice: a central pitch, a higher pitch for emphasized words, and a lower pitch at the end of a phrase or sentence. Try assigning those pitches to three notes, and see if that works as a melody. Adjust the notes as you need to so that they fit your chords. Sometimes that's all you have to do, and the melody falls into place.
Using the natural melody of speech is easy for you as a songwriter, and it also makes it easy for the listener to grasp the meaning of the words. You can't use this technique all the time — some songs demand something different — but go ahead and use it where you can.