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You requirements are too clear. Are you looking for an eInk device or just small tablet device that can sync with Google books?
Right now sync is not supported across different companies. Sync can only be done withing the app of the company. For instance all kindles support sync but only amongst kindles. Google, SONY, B&N are the same.
That said the previous poster suggested the iRiver because that is the only eReader with eInk that supports google books.
If you just want a bigger screen and are willing to read off an LCD screen any Android base tablet will work.
However if you want an eInk screen you really have two choices. The iRiver or root an Android base eInk like(nook touch or the Sony Reader). Both of those devices have been rooted and have methods to install the Google Reader app.
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