This is something else ITA Matrix can help with. While it won't show award availability, it does have the ability to look for routes limited to a specific alliance. For your search it would look like:

Click on Advanced Routing Codes to open the box and enter:

Departing from = DAY,CHM [adding as many as would work for you]
/ alliance star-alliance

Destination = TNR
/ alliance star-alliance


For the random dates I chose I was returned 17 pages of options.