Whether parodies constitute fair use is an extremely complicated and fact-intensive question, at least in the United States. I think everyone who reads newspapers has heard about "The Wind Done Gone," where if memory serves me right, the 11th Circuit overruled the District Court which had decided it infringed the copyright on "Gone With the Wind." If you are in the United States, and copyright holder is prickly or rich, it's not a bad idea to consult a lawyer.

If you'll excuse a dumb question, what is a "cover"?