Sometimes when I'm stuck in my songwriting, I do something very simple: I take the melody I'm working with and try it with both major and minor tonal centers underneath.
For example: in the below video I take a piece of the folk song "Shenandoah", which is traditionally in a major key. Just to shake things up, I try it using the relative minor.
If your song is in C Major, try it in A Minor. If your song is in D Minor, try it in F Major. And so on.
To find relative minor or major keys, see the circle of fifths.
In fact, the circle of fifths is a personal favorite item of mine. When I get stuck, I use it to experiment with all sorts of chord progressions. I look across the circle, I close my eyes and point, I go as far away from the tonal center as I can and see how I can get back, etc. Whatever strikes my fancy. My students call the circle of fifths "The Vortex", because the longer you look at it, the more relationships start appearing. It's a lifetime of never-ending learning and fun!! (what can I say, I'm a bit of a theory dork).
At any rate, see below for a simple example. (When I say "Make a melody major", what I mean is, make the harmonies underneath it major, etc). Enjoy!