http://cisco.com/en/US/products/sw/voicesw/ps2237/products_installation_guide_chapter09186a00801ba67e.html
To Move the Cisco Unity UMR
Step 1 Start Regedit.
Step 2 If you do not have a current backup of the registry, click Registry > Export Registry File, and save the registry settings to a file.
Step 3 Expand the key
HKEY_LOCAL_MACHINE\Software\ActiveVoice\UnityUMR\1.00.
Step 4 Double-click MtaFailedPath, and set the Value to the new location.
Step 5 Click OK.
Step 6 Expand the key
HKEY_LOCAL_MACHINE\Software\ActiveVoice\UnityUMR\1.00.
Step 7 Double-click MtaStoragePath, and set the Value to the new location.
Step 8 Click OK.
Step 9 Restart the Cisco Unity server.
So what else is on your c-drive? Perhaps you have exchange database and logging on that drive too.
Moving Exchange Message Stores and Transaction Logs to an Alternate Drive
http://cisco.com/en/US/products/sw/voicesw/ps2237/products_tech_note09186a00800c6f5f.shtml
Then there is the pagefile. You can move that to the d-drive but the caveat is that "If you move the Paging file from the system partition, Windows cannot write debug information to the disk in the event of a "Stop Error" message (blue screen error)"
Moving the Windows Default Paging and Spool File
http://support.microsoft.com/kb/123747/EN-US/