Duke maintains a searchable list of internal and external funding opportunities: https://researchfunding.duke.edu/
Fellowships available to U.S. citizens and permanent residents only
The Hanna H. Gray Fellows Program (PhD applicants can have no more than 16 months of postdoctoral research experience at the time of the application due date)- supports early career life scientists in academic labs across the U.S. Seeks to increase diversity in the biomedical research community. We know that the biggest challenges in science call for diverse perspectives and original thinking. The goal of the Hanna H. Gray Fellows Program is to recruit and retain individuals from gender, racial, ethnic, and other groups underrepresented in the life sciences, including those individuals from disadvantaged backgrounds. https://www.hhmi.org/programs/hanna-h-gray-fellows-program#Eligibility
NSF-Postdoctoral Research Fellowships in Biology (PRFB)- The fellowships encourage independence at an early stage of the research career to permit Fellows to pursue their research and training goals in the most appropriate research locations regardless of the availability of funding for the Fellows at that site. For applications under this solicitation, these areas are (1) Broadening Participation of Groups Underrepresented in Biology, (2) Interdisciplinary Research Using Biological Collections, (3) National Plant Genome Initiative (NPGI) Postdoctoral Research Fellowships and (4) Integrative Research Investigating the Rules of Life Governing Interactions Between Genomes, Environment and Phenotypes.
https://www.nsf.gov/funding/pgm_summ.jsp?pims_id=503622
Hartwell Foundation Postdoctoral fellowship
https://researchfunding.duke.edu/hartwell-fellowship
Fellowships available to U.S. citizens and International postdocs
Damon Runyon (<1 year after Ph.D)
Jane Coffin Child (<1 year after Ph.D)
Helen Hay Whitney (<1 year after Ph.D)
Cancer Research Institute (< 5 years after Ph.D, but < than 3 years in lab)
Life Science Research Foundation (< 5 years after Ph.D)
American Heart Association (< 5 years after Ph.D)
Regeneration Next Initiative Postdoctoral fellowship (<1 year after starting at Duke)
Brain and Behavior Research Foundation (postdoc research relevant to psychiatric disorders)
This website from UC Berkeley covers a number of other funding opportunities - https://spo.berkeley.edu/fund/biopostdoc.html