When Google shutdown their reader service last year they really pissed off quite a few people. Many ended up moving to Feedly and other services that popped up over time. One of the options that came out then was Tiny Tiny RSS which is an open source project that allows you to host your own Google Reader clone on your own server so it never gets shut down.
Now Marcel Meissel has come out with TE-Reader for Tiny Tiny RSS which is a nice client for Tiny Tiny RSS. This is about the closest you are going to get to a full Tiny Tiny RSS reader for BlackBerry especially if you are looking for a native one. Check out TE-Reader free in BlackBerry World at this link.
Thanks EJ for the tip!