If a resume can't convince them to hire you, what made you think a cover letter can? Also, no recruiter spends over a few seconds glancing at your resume? So, throw another doc at them?
I think every job I've ever applied to has asked for both a resume/CV and a cover letter. A recruiter may glance at first but if they like what they see or they can only put through 10 applicants to interview then they're likely to properly read through.