Funding opportunities for postdoctoral scholars of all levels, from those just defending their PhD to those transitioning to their first faculty position are available on this page. A job board site is available to Postdocs (and graduate students) called Biocareers: not yet available.
Here is a great list of funding opportunities for postdocs:
Are you on a H1B visa and thought you could not apply for a fellowship?
That may not be true! There are some funding agencies that are willing to pay employee salaries through the university (rather than a stipend to you directly). If a fellowship is particularly well suited for your research and citizens from your country are eligible, you may contact the funding agency to ask if they will pay salary rather than stipend.
Examples of funding agencies that have paid fellowships as salary to H1B visa-holders in the past are: