I'm looking to suppress caching for all files that end with .appcache in IIS.
If I was using Apache, I would drop the file into a directory and add:
ExpiresActive On ExpiresDefault "access"
How do I control caching headers in IIS?
You can write Cache Rules in IIS and add the extensions that you'd want to manipulate and specify the actions which need to be performed on the files with those extensions.
Select the hostname --> Select Output Caching --> Add the extension ".appcache" --> select the "prevent all caching" or uncheck "user-mode caching" and it should stop IIS from keeping a cache of the pages.
Hope this helps.