Application pool Identity with a custom Windows account.
Configuring the application pool Identity to a custom Windows account, specifying the Identity (DOMAIN_NAME\USER_NAME), as well as the password.
PS: In the meanwhile, maybe you can write and share with us some IIS PS scripts to run after deploying the web site?
AdminEmma A (Admin, Red Gate) commented
A PowerShell script to do this has just been added to the PowerShell forum which might help, http://www.red-gate.com/messageboard/viewtopic.php?p=64762#64762