I need to customize date picker in a script toolbox so base on the input data, user could pick a date or different dates to do some process.
Python only interfaces with tools in arctoolbox in that it can call a tool. Or there is the arcpy module and there is no reference to data picker. Perhaps you had better clarify or show what it is you need.
Did you get a reference somewhere that python could be used? or were you just hoping to use python?
I think you are referring to what's known as a comb-box: a pick list that is pre-populated with values. (Think attributes domains values). I've used them in python addins, but I've not used hem in a script tool. However, check this out: arcpy - Choosing string from dropdown list rather than typing it into Python script tool? - Geographic Information Syste… It describes:
Set the data type to string and change the filter type from None to Value List. Here you can add in all the values you want to see in a drop down list.
Setting script tool parameters—Help | ArcGIS Desktop
Setting script tool parameters—Geoprocessing and Python | ArcGIS Desktop
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