Even if you don't *need* a cover letter, some positions might really prefer to see one and it's great experience to practice with using one for when you are applying to jobs post-internship/college.
Also, some roles won't require one but based on the role I would highly recommend it. I applied to PR and Marketing positions, and got three interviews (Social Media for Youth, Social Media for Fairytale Weddings, and Sales and Travel Ops PR) and got offered the Sales and Travel Ops PR position. Not saying the cover letter I submitted was the deciding factor in any of it, but I suspect it helped.
When I submitted my apps for PIs, I had the cover letter as the first page of my resume. So cover letter on page one, followed by full resume on page two. If you chose to go this route, I would highly suggest saving the document as a PDF and submitting it that way. This way you won't have to worry about microsoft word mucking up your formatting. This is actually a good recommendation for any online submission job apps, because word can really make your resume look like a mess if the person opening it is running a different operating system than you.