Break out your family tree. Is there someone in your extended family who might have the resources to lend you a hand? What you want to get across is that you're not looking for a handout, but a relationship to which you'll be able to contribute significant value. Maybe your grandfather has always wanted someone in the family to become a draftsman as he was. Or perhaps you have a great-aunt who would welcome the promise of someone to take care of her husband after she passes away. Whatever the situation, your goal is to find a need and demonstrate your willingness to be supportive.
Enlist your identity as a resource. If you are a member of a minority group, perhaps there's an organization that would contribute to your cause. Additionally, there are many so-called "unusual" scholarships offered which may apply to you.
Choose a specific path. It's much easier to convince someone to help when you have something specific in mind and a plan that will get you there. Of course, this may mean narrowing your options depending on your benefactor's preferences, but that's not necessarily a bad thing. There are scholarships specifically for students who want to become teachers, for aspiring female engineers, and for biologists. If you're willing to make that kind of commitment, that can only enhance your chances of finding someone to take your side.