I've got an old Kawai with pre-programmed background rhythms. They are pretty basic but they do repeat.

Now, if you have a computer anywhere near your teaching studio... I can help you with some software that you can use for the same purpose. Either "band in a box" (VERY cheesy, but also very easy to set up - according to flattop) or "fruity loops" (a very cool program, but can be less easy to learn).