Refer to the ATA 186/188 administrator guide for information on STUN support.
http://www.cisco.com/en/US/docs/voice_ip_comm/cata/186_188/3_0/english/administration/guide/sip/SIP88CH4.html
Cisco devices use a different method to avoid having to use STUN in the first place, using the VIA: option so they can
register correctly with the SIP server. You'd configure this per this doc on the ATA:
Look under "receiver tagged VIA header"
http://www.cisco.com/en/US/products/hw/gatecont/ps514/prod_release_note09186a0080109764.html
To maintain NAT/PAT translation for a session, the Cisco ATA 186 can now be configured to periodically send dummy UDP packets to a server (the Cisco ATA 186 does not expect any response from the server).
Here's some NAT related information that may help you with your situation:
http://www.cisco.com/en/US/products/hw/gatecont/ps514/products_administration_guide_chapter09186a00800c4b87.html
(see "NAT Gateway" and "NAT/PAT Translation" )