There is relatively little funding of the sort you are looking for--funding that non-U.S. residents can apply for directly to fund post-doctoral work inside the U.S. However, that is not really that important, since that is not how most post-doc positions are funded anyway.
Most post-docs do not apply for their own funding. The funding comes from the institution that hires the post-doc (Very often--but not always--the money ultimately comes from a research grant from an outside agency, but the post-doc would not be involved in writing or administering the grant.) If an institution has funds for a post-doc, they will advertise a job opening and hire somebody. Generally, the search is global; they would be willing to hire somebody from anywhere in the world, provided they are a qualified. (There are some technical caveats about how this works, but they are of little import in practice; and--again--they are things that the hiring institution mostly needs to worry about, not the person they choose to hire.)