Well since you have a regular nook isn't your tablet registered to same account? Therefore access to same books?
For me I just did the Dropbox online calibre library.
1) Installed Dropbox app on my computer. And made folders for pics,music,etc,,
2) Installed Dropbox app on my Nook.
3) Found the Calibre Libray folder and copied whole folder to my Dropbox folder. Shows up as E:\Dropbox\Calibre Library\ for me. (Note: Depending on number of books and your internet connection can take a while to upload to your account) Also free account is limited to 2gb.
4) Started up Calibre used the setup wizard or perferences to point to cloned library in dropbox folder.
Now anytime I add a book to Calibre is automatically uploaded to dropbox account. And any device that has the Dropbox app can access and download to device.
That way don't have to have device hooked up to computer. And can add books anytime to Calibre and then download them later or more convient time without plugging into computer.
Not sure what Drop Box app is where do I get this. As far as syncing goes. I am not a computer literate person. With the many different types of ereaders we have I needed a library that supports all format, Calibre is awesome for that reason. Any books I have had for years in pdf format was easy to convert. All I have to do is plug in whatever ereader needs books and the Device Icon appears then highlight the books I want and click send to device and they are there. However when I plug in the new nook color tablet the Device Icon never appears would anyone know why???