Wiki instance mirrored to another box
Just my 2 cents:

You could set up a MySQL master-slave replication, the master being inside the internal network and the slave on the external site.

You could also do a nightly mysqldump of the wiki, sftp it to the external site via a cron job and restore it there, but it looks like an ugly and clunky solution to me.

Perhaps the simplest thing would be to give up mirroring and have the wiki on the external site only, so it would be accessible in case of internal network downtime.