So a wild guess is that this carrier method is not available or is actually deprecated. As the line in the file /app/code/core/Mage/Usa/etc/config.xml is as follows.
<specificerrmsg>This shipping method is currently unavailable. If you would like to ship using this shipping method, please contact us.</specificerrmsg>
Try using only the carrier with the code dhland label DHL and not the DHL (deprecated) version.
Best Answer
There is Free extension avliable please install this extension for your purpose
https://www.magentocommerce.com/magento-connect/dhl-auspost-startrack-fastway-couriers-please-shipping-extension.html
this extension provides you
DHL ,AusPost ,StarTrack, Fastway Couriers
integration please check this if its fit to your requirement install and check