Yes, there are funds available specifically for producing captioning. While the U.S. Department of Education is still a major source of caption funding, a good deal of captioning today is made possible by corporate support. Corporate contributions supplement or match those allotted by a program's producer and its distributor (i.e., the broadcast or cable network or syndicator). Contact the Media Access Group for more information about becoming a corporate sponsor, or to learn more about grant-funding opportunities.
3PlayMedia, on its web page 5 Ways to Pay for Captioning with Grants and Funding, provides a list of grants and other awards that can fund closed captioning.
Sometimes, state governments, or groups of colleges/universities within a state, make funds available, so checking in your geographic area is a good idea.
In addition, some small businesses may be eligible for a federal tax credit for providing captioning. For more information, consult Tax Benefits for Businesses Who Have Employees with Disabilities.
To locate captioning service providers, consult the DO-IT Knowledge Base article, Where can I find vendors who provide captioning services?