Hey there. I wanted the same thing - you can get pretty close to the functionality you describe if you use Dropbox in addition to Calibre.
Basically, set up your Calibre library within your Dropbox folder. Set Calibre up to grab feeds however often you like.
Since your Calibre library is in Dropbox, the files it creates from the feeds become accessible on the web. Use the Sony's browser to access Dropbox on the web (the mobile Dropbox site looks pretty good on the Sony's browser), and download from there.
If you set up each feed individually in Calibre, you'll end up with lots of files to download. If you find that annoying, you can solve it by putting your feeds all into Google Reader, and having Calibre grab your Google Reader feeds as a single file.
So overall, you're setting things up like this:
1. Feeds into Google Reader
2. Google Reader into Calibre
3. Calibre to Dropbox
4. Dropbox web access to the Sony.
The first three steps will all happen automatically but I haven't found any way to make step 4 happen by itself. And I suppose if you have lots of ebooks (and manage them all with Calibre) they might not fit in the free Dropbox account.
Still works better than anything else I've found, though
Good luck!