This was discussed on the “Project Coin” mailing list. In substance (emphasis mine):
Internally, a Java compiler operates over a richer set of types than
those that can be written down explicitly in a Java program. The
compiler-internal types which cannot be written in a Java program are
called non-denotable types. Non-denotable types can occur as the result
of the inference used by diamond. Therefore, using diamond with
anonymous inner classes is not supported since doing so in general would
require extensions to the class file signature attribute to represent
non-denotable types, a de facto JVM change. It is feasible that future
platform versions could allow use of diamond when creating an anonymous
inner class as long as the inferred type was denotable.
Note that it is not supported in Java 8 either but will be included as a new feature in Java 9 (Item 3 of “Milling Project Coin”).