@Mrs.-AMBIKA (Note, the answer to this question is pretty similar to the Constant voltage/current mode question.)
I think the Cheapstat hardware is capable of doing what you want. There is a constant voltage test available in the firmware which will set the potential of the working electrode for a given duration. Both the potential and duration are something the user can adjust. There are a couple of caveats. As far as I can tell the constant voltage test doesn't send any data back to the PC after running - so you don't get a current measurement. I'm not the original author of the firmware, but my guess is that the constant voltage test was designed for testing the voltage output of the Cheapstat rather than it was for making measurements.
As another possible option I did at one point create a quick-and-dirty modification of the cheapstat firmware which adds a long duration constant voltage mode which might work for you. In this case the device does stream back current data to the PC. More details can be found here http://forum.iorodeo.com/topic/5/constant-voltage-current-mode