Can't this be done by taking a db-backup from Admin-panel on the site, and then import the db-backup via phpMyAdmin and import it in the right language/character ??
I do this for both my own sites and for my users on my site too. Sometimes we have problem with showing tha danish letters æøå/ÆØÅ on some servers. I work around this by importing the db-backup in phpMyAdmin and then choose for character Latin1 (for us Danish users).
Yes, I do like smokeman : save the DB with the option "drop table if exists", use a nice text editor (I use Notepad++), convert to UTF-8 (Notepad++ has the feature), save and re-import the DB while carefully chosing the import charset in PHPMyAdmin. But you still have to do what bdo stated to avoid mixing charsets in the future.