I assume you are going through Recruitment at Bama. I am very familiar with their recruitment process and I recommend that you send a picture and resume to all the sororities that you don’t have recommendations for. If don't have a recommendatioin for the house and the women see you resume and like, they'll try to find someone to write you a recommendation, also some of the houses it is hard to find recommendations for. Also if your grades are border line send official transcripts. Send them directly to the recomendation chairs. You can find those address on their website at
www. bama.ua.edu/~npc. Whatever you do don't send them to the Panhellenic office, because they will throw them out.
I was on Panhellenic when I was at Bama, and now I'm serving as a Recruitment advisor.
Good luck during recruitment!
Don't worry about a cover letter.