Cover letters aren't hard. At all. I have a generic cover letter that I tweak a little bit for each company. Fill in the position I'm applying for, explain relevant experience, say that I'll "help the company $WHATEVER_THEY_DO", and if I'm particularly interested in working for the company, explain why. It takes 5-10 minutes tops. I don't think there's ever been a time that I didn't get a response when the job was particularly interesting. People tend to want to hire people who want to do the job.