Given a date obtain latitude and longitude where is the sun zenith
What you're looking for is the latitude and longitude of the subsolar point.

Calculating it with accuracy is somewhat complicated.  Here is a python library that has routines to do it for you:
http://rhodesmill.org/pyephem/

You could also possibly query this information from other sites.

If you really want to work it out on your own, I suggest "Spherical Astronomy" by Robin M. Green published by Cambridge University Press as a starting point.