Is there a way to enable Java only for specific applications? I know that it is possible to completely disable Java in OS X, and to disable its use from within a given browser. I use just one or two applications that require Java, and would like to enable it for them, but prevent it from running in all other cases.

Is there a way to enable Java only for certain apps that I specify?
There is a way, but it's convoluted and non-intuitive.  I will say that I do not recommend this approach, but I am listing it for completeness.

Java Default Policy Administration is the official doc on Java's own internal security and access policy.

The idea is that you can set deny access to files/folders at a global level, then add specific grant permissions to those Java classes/jars you want to allow.

The permission's that can be set are listed in the JDK Permissions  

Some examples of what can be done can be found at ExampleDepot