Inventory is a global level attribute in Magento 1 & 2 (for now) and so this is not possible. The way around it is either to have separate installations (that could be running on the same codebase deployed to a separate location with a different database) or through an extension.
I don't have familiarity with any of them but there are a few around on Magento Connect:
https://www.magentocommerce.com/magento-connect/multi-location-inventory.html
https://www.magentocommerce.com/magento-connect/multi-warehouse-inventory-management.html
https://www.magentocommerce.com/magento-connect/inventory-management-for-multiple-locations.html
----
If you've found one of my answers useful, please give "Kudos" or "Accept as Solution" as appropriate. Thanks!