Programmable Logic Controller
The requirement described may be met by a set of 4 H-bridges, one per magnet, all controlled by a microcontroller. 

Each H-bridge can then be switched into one of two opposite coil current directions, or open-coil, or shorted-coil, independently. 

This meets the following points:


Polarity - coil current direction
Time on/off - by the microcontroller
Order - as above
Controlled by laptop: 

Just incorporate a serial control parser into the microcontroller code, assuming your development board of choice or custom board has some USB to serial interface; most dev boards do.

Fairly simple programming language: 

C is pretty simple, and is available on most microcontrollers. 
Alternatively, use something like the Parallax BASIC Stamp, which supports a form of BASIC. 



There isn't a pure computer-based approach that comes to mind for something like this.