Just changing the type of the node in the {node} table is not enough -- an entry also needs to be made in the {book} table. The example below assumes your database table prefix is drupal_ and that you want to change node 1234 to a book node.

UPDATE drupal_node SET type='book' WHERE nid=1234;
INSERT INTO drupal_book (vid,nid) VALUES ((SELECT vid FROM drupal_node WHERE nid=1234), 1234);