The Landeskirchliches Archiv in Stuttgart has many records of Württemberg in their possession. However, they will not do extensive research for patrons. They will provide you with a list of professional genealogists that can be hired for your family research project.
This is what you can accomplish through the above mentioned
http://www.archiv.elk-wue.de/cms/startseite/family-research/
Here is a list of district archives which houses the records of the older administrations of Württemberg (click on name of archive and then on Beständeübersicht to look at the holdings)