I am a 17yr old girl that has been emancipated and have run in to this question myself. I have found that most banks cannot issue a credit card to a minor, emancipated or not, unless they offer special types of accounts. Bank of America, whom I bank with, offers a student credit card that you can apply for if you are registered or currently attending a college or university.
After graduating at 16 I applied for this type of account and was informed that unless I have a parent or guardian co-sign I could only be issued a debit card. After my emancipation and registering for a local community college I could be eligible for the credit card however. I now have a student credit card with Bank of America, it was very easy to apply for after I brought in my certified copy of my emancipation and proof that I had registered for the college.
What I can recommend is ask around at different banks and see what they have to offer for emancipated minors, most banks will turn you away until you are 18 but if you are attending college or plan to do so soon Bank of America can help.