In Java, can I declare a HashMap constant?

Yes, it can be a constant. You should declare your HashMap instance as follows:

class <class name> {
    private static final HashMap<Integer, String> tensNumberConversion = new HashMap<>();

    static {
        tensNumberConversion.put(2, "twenty");
        tensNumberConversion.put(3, "thirty");
        tensNumberConversion.put(4, "forty");
        tensNumberConversion.put(5, "fifty");
        tensNumberConversion.put(6, "sixty");
        tensNumberConversion.put(7, "seventy");
        tensNumberConversion.put(8, "eighty");
        tensNumberConversion.put(9, "ninety");
    }
}

However, this is only a constant reference. While you can not reassign tensNumberConversion to something else, you still can change the contents of your map later at runtime:

tensNumberConversion = new HashMap<>(); // won't compile
tensNumberConversion.put(9, "one"); // succeeds

If you want the contents of your map constant too, you should wrap the HashMap into an unmodifiable map:

class <class name> {
    private static final Map<Integer, String> tensNumberConversion = initMap();

    private static Map<Integer, String> initMap() {
        Map<Integer, String> map = new HashMap<>();
        map.put(2, "twenty");
        map.put(3, "thirty");
        map.put(4, "forty");
        map.put(5, "fifty");
        map.put(6, "sixty");
        map.put(7, "seventy");
        map.put(8, "eighty");
        map.put(9, "ninety");
        return Collections.unmodifiableMap(map);
    }
}