American Council of Learned Societies
Andrew W. Mellon Foundation Grants Database
Council on Library and Information Resources Mellon Fellowships
Digital Humanities Advancement Grants
Institutes for Advances Topics in the Digital Humanities
Many major US research funders have public access requirements for any publications and data stemming from grant funds.
Many journals also have policies requiring open access to research data for the purposes of replication and further research. Open Access Directory lists many journal open data policies.
American Psychological Association
CLIR Postdoctoral Fellowship Program
Institute of Museum and Library Services