We have a MySQL instance setup on a server that we then allow students to create databases on.
Have just installed each particular student as a user who only has control of one database ( same as their username ).
They can then add table / run SQL etc....
We also use PhpMyAdmin, again installed on server, to allow the students to control their database but I am currently looking at some of the GUI tools and might install these onto student desktops.
Hope this helps.