Use ancient Altera MAX II board in modern environment
Unfortunately no.

There is no way to modify Quartus to work with an unsupported device. You'd have to find an older version of Quartus which supports the device and use that.

Alternatively, and probably more sensibly, you could upgrade to a more modern device. There are for example many Cyclone V based dev kits that are pretty cheap, though I'll let you search for something. 

If you are trying to teach FPGA based stuff, using an ancient device, especially one which is an engineering sample, is possibly not the best course of action - you'd spend more time battling bugs and glitches in the tools (if you can even get them set up) than you would teaching.