I agree with the suggestion of 2. Unless she is a legacy or has a number of relatives (cousins, aunts, etc) of a certain sorority, 2 should be plenty. But of course, a minimum of 1.
If she doesn't know a member or alumnae of each sorority, she needs to seek out the local Alumnae Panhellenic in her area...and the sooner the better since they are probably pretty busy writing recs. Tell her to send her resume, a photo, and a cover letter...they might even have a form on their website that she needs to complete.
I believe Ole Miss has links on their Recruitment site telling girls how to get recommendations.
Good luck to your cousin!