RSS Feeds for Private Sites

We are trying to use the RSS widget to show feeds between private sites which require a login.
On open sites, this works as expected. I thought that maybe that feed keys could be used, but there isn't this option.

On the RSS Widget, when we put in the feed address if a private site, I see the error message: RSS Error: A feed could not be found at http://url. A feed with an invalid mime type may fall victim to this error.

Is there a way to get feeds from private sites working?

I looked at private feed keys and Private RSS Feeds which support found, but they don't work the way I need them, which is easy!

Thanks,

Matt