The Brown University Library offers a Library Resource Guide for Grant Resources that includes access to subscription services, such as SPIN, a database of opportunities from federal, governmental, international, private and corporate funders. These resources are accessible via an on-campus workstation with a Brown NetID and password, or off-campus by logging in through a proxy server. For assistance with off-campus access, contact Computing and Information Services.
Another source is Pathways to Science.
The Open Education Database offers a list of 100+ Places to Find Funding For Your Research.