I'm playing the PC version with an XBox controller. The middle Xbox ring button would be ideal for quick save in this game! :)
The "Xbox" button in the center of the Xbox 360 controller is sometimes a special button that is caught outside of the game, especially in games that use Games for Windows Live. I haven't found any tutorials for remapping Xbox 360 controller buttons on the PC that were able to remap that particular button. However, if there is a way to do it, it will likely be via AutoHotKey, which I've covered in a couple of other answers.
More than likely, it'll just be a matter of rebinding that button on the controller to whatever the "quicksave" key is in Skyrim. (I believe it is F5 by default.)