Having interned with both a regional airline and a major airline...skip an unpaid regional internship and seek out a major/legacy airline internship (paid or not) if you have even a passing interest in 121.
There are a handful of 91 departments that have done internships in the past - IBM, United Technologies, Coca-Cola and Limited Brands come to mind off the top of my head...there likely are a number of others.
If there is a particular department or location you are interested in, it does not hurt to make contact with the Director of Aviation or Chief Pilot and ask the question - may lead to nothing, may help develop a long-term mentorship or networking contact, might end up with you in an internship.