Is there a reliable indicator for which which NIH RFAs are open to post-docs? I haven't found any guidance on NIH's websites so far whether or not someone who has a Ph.D. but is not yet full-time faculty (e.g. post-doc) is eligible to be named as a co-PI on an R01 grant. 

For that matter, the individual eligibility criteria are really vague-- it's not clear that they even exclude a post-doc from being a sole PI on an R01 grant. That makes me think that I'm looking in entirely the wrong place to see if I am eligible for a given RFA.

Is there a foolproof indicator of whether or not a given RFA is open to post-docs either as sole PIs or co-PIs?

Thanks.
Ask your institution's Sponsored Research Office (SRO). These organizations are often called by other names like Office of Sponsored Projects (or Programs), the Sponsored Programs Office, or something similar. It's their job to understand the rules and regulations associated with external grant funding for research institutions. 

In my experience with NSF (not NIH), the eligibility requirements for institutions and PIs are spelled out in each RFA/RFP. I have frequently seen limits on the number of proposals that a PI or institution can submit, and there are frequent limits on the types of institutions that may submit (e.g. 4-year, degree granting colleges and universities only, etc.), but I have never seen a limit in the RFA/RFP for the qualifications of the PI or co-PI. 

My institution, however, does put limits on who may submit. Post docs, as far as I can remember, are not given blanket authorization to submit. They, and even more junior staff, are allowed to submit grant proposals only with an exception as approved by their unit head (dept. chair, center director, etc.) and, I think, the VP for Research's office. These are, in my experience, always granted for post docs.

That being said, the proposal preparation guide requires you to describe your qualifications for submitting the research, including prior work, prior grant support, and other relevant material. If you haven't been a co-PI before, a proposal with you as PI probably won't look as strong to the review panel. It's probably best to start as a co-PI with a more senior, experienced researcher as PI. This is true even if you will primarily lead the day to day work of the project.

This is all based on my experience with NSF, but I don't think NIH is much different.