Creating custom stamp

Acrobat X already comes with a number of dynamic stamps that include the date (e.g. Revised and Approved), which you can modify. See here for instructions about how to modify one of these built-in stamps: Modify Dynamic PDF Stamps in Acrobat - KHKonsulting LLC

All you need is this little JavaScript snippet to print the date in a field (this is from the Revised stamp):

event.value = (new Date()).toString();
AFDate_FormatEx("h:MM tt, mmm dd, yyyy");

All you need to do is change the time/date format to whatever you want (e.g. just "mm dd, yyyy" for the date).