How does one instantiate an array of maps in Java?

Not strictly an answer to your question, but have you considered using a List instead?

List<Map<String,Integer>> maps = new ArrayList<Map<String,Integer>>();
...
maps.add(new HashMap<String,Integer>());

seems to work just fine.

See Java theory and practice: Generics gotchas for a detailed explanation of why mixing arrays with generics is discouraged.

Update:

As mentioned by Drew in the comments, it might be even better to use the Collection interface instead of List. This might come in handy if you ever need to change to a Set, or one of the other subinterfaces of Collection. Example code:

Collection<Map<String,Integer>> maps = new HashSet<Map<String,Integer>>();
...
maps.add(new HashMap<String,Integer>());

From this starting point, you'd only need to change HashSet to ArrayList, PriorityQueue, or any other class that implements Collection.

You can't safely create a generic array. Effective Java 2nd Edition goes into the details in the chapter on Generics. Start at the last paragraph of page 119:

Why is it illegal to create a generic array? Because it isn’t typesafe. If it were legal, casts generated by the compiler in an otherwise correct program could fail at runtime with a ClassCastException. This would violate the fundamental guarantee provided by the generic type system.

To make this more concrete, consider the following code fragment:

// Why generic array creation is illegal - won't compile!
List<String>[] stringLists = new List<String>[1]; // (1)
List<Integer> intList = Arrays.asList(42); // (2)
Object[] objects = stringLists; // (3)
objects[0] = intList; // (4)
String s = stringLists[0].get(0); // (5)

Let’s pretend that line 1, which creates a generic array, is legal. Line 2 creates and initializes a List<Integer> containing a single element. Line 3 stores the List<String> array into an Object array variable, which is legal because arrays are covariant. Line 4 stores the List<Integer> into the sole element of the Object array, which succeeds because generics are implemented by erasure: the runtime type of a List<Integer> instance is simply List, and the runtime type of a List<String>[] instance is List[], so this assignment doesn’t generate an ArrayStoreException. Now we’re in trouble. We’ve stored a List<Integer> instance into an array that is declared to hold only List<String> instances. In line 5, we retrieve the sole element from the sole list in this array. The compiler automatically casts the retrieved element to String, but it’s an Integer, so we get a ClassCastException at runtime. In order to prevent this from happening, line 1 (which creates a generic array) generates a compile-time error.

Because arrays and generics don't combine well (as well as other reasons), it's generally better to use Collection objects (in particular List objects) rather than arrays.