I don't know who decided all resumes need a cover letter. Half of the cover letters I've read simply put the resume into paragraph format, and the other half just said, "See attached." To me, the cover letter is like the little sock an umbrella comes in: It makes the umbrella look slightly nicer before you open it, but the umbrella itself is doing the real work. Also, you'll probably lose the umbrella sock at some point, and you'll notice no deleterious effect on your life.
Sure, many cover letters qualify as true umbrella socks. The "Dear Sir or Madam" letters, the "See the enclosed CV" letters, and so on. On the other hand, perhaps its because of this general low-level impression of cover letters that the really good ones can stand out. That's why they are valuable. When well-written, and directed to a particular individual, they are read and not quickly scanned as is the CV. They can make a difference. They can take a point that is buried in the middle of your technical jargon on the CV and illuminate the real-life impact that this skill or experience brings to the table.
Don't give up on cover letters.