Right... start by deleting stuff or moving it off the drive. Once the contents tke up less space than the formatted capacity of the new drive, try CCC or SD again. If that does not work, then try my above suggestion of shrinking the partition first.
Think about it reasonably... if you have a bookshelf, and it holds 200 books right now, and it's full, and you throw it away and go out and buy a new bookshelf that's half as big, why would you expect all your old books to fit in it?