I understand that MCNY does not offer on campus housing but do I still need to show that I can provide for housing on my own?

Yes, in order to be issued an I-20 to apply for a student visa in your home country, you will need to show proof that you can cover tuition expenses as well as the estimated expenses for housing and other fees. Although, MCNY does not directly charge you for these estimated expenses, all students should be able to demonstrate adequate funding for living and personal expenses apart from the cost of attending MCNY.