"This is the one of my favorite songs due to its sweet lyrics yet sorrowful melody."
You do need "songs" to be plural. Also, "sweetful" is slightly slangy and sounds funny in a sentence.
If you use "for", you're suggesting a purpose. "This is the one of my favorite songs for when I'm driving to work." The relative clauses that have been suggested are understandable, but have the effect of separating the sentence - they sound a little impersonal to me. I suggest "due to" because it connects the two parts of the sentence well.
The way I used "yet" is slightly uncommon but valid. The sentence is slightly condensed at the end, but now has a poetic feel. "Technically proper" expressions would destroy the emotion of what you want to say.