Well, yes that's very understandable since he doesn't pronounce a lot of his lyrics clearly. I'm just helping with correction. Any objections?

"I just want to dream quietly, quietly, quietly..." umm no. Let's look at this.
"shizuka ni shizuka ni tada shizuka ni yume o mite iru"
First off, 'miru' is in the 'te iru' form. He is now viewing.
Second, 'want' is not even mentioned in the sentence. So, most literally:
"Quietly, quietly, I'm just quietly viewing a dream" (or just quietly dreaming)
Any objections?