The college or university at which you are completing your PhD likely has scholarships available or at least the opportunity to apply for that funding, however scarce. Moreover, most PhD students also receive a stipend from their educational institution, and that stipend can go toward the cost of living or to facilitate further academic research. Different departments of a university also offer funding for student projects. Consult with the director of the department for more information about funding and scholarship opportunities.
Numerous scholarships are also made available by public institutions like the National Science Foundation. In particular, the National Science Foundation provides links to more research scholarships. (References 1) For those most interested in the social sciences or the humanities, the U.S. Department of Education publishes a list of publicly available scholarships. (e.g. Fulbright Scholarship, Boren Fellowship, etc.). The National Endowment for Humanities also provides scholarships for the arts and humanities. (References 2)
Private scholarships are provided by nonprofits, as well as corporations that might want a stake in your research. For the social sciences especially, think tanks offer a number of fellowships and scholarship opportunities to continue your research (e.g. Brookings Institution, RAND Corporation). Corporations, on the other hand, are more likely to provide funding support for an employee who seeks to continue relevant academic research and then return to the corporations (e.g. support for an employee's enrollment at a business school or toward a PhD in economics or support for a continued PhD in science if working for the corporation's product development division).