Convert cooper to S model

Not sure what you mean by convert? Even if you transfer parts from an S model, the car will still be a base model (by VIN).

What are the parts I need to make my base virtually the same as a cooper s. (what is specifically different between the cooper and the cooper s?)

I found this on Edmunds.com: "The Cooper S hatchback adds a more powerful engine, 16-inch wheels with run-flat tires, firmer suspension tuning and sport seats (optional on the base Cooper). The Cooper and Cooper S convertibles differ from the coupes mostly by offering a power-retractable soft top (with a sunroof function) and rear parking sensors, but do not come standard with an auxiliary audio jack, while the telescoping wheel and Sport settings are not available."

I think you will find it is not worth trying to change your car. Read for yourself on this page: https://www.edmunds.com/mini/cooper/2008/