What you could do, is store your resources into a List, then randomly permutes it thanks to Collections.shuffle(List<?> list) or shuffle(List<?> list, Random rnd), and finally call iterator() on the resulting list to get an instance of Iterator that you could store into a member field to be able to iterate over your list (thanks to hasNext()/next()) and remove your resource once done with remove().
Here is a pseudo code using String as resource just to show the idea:
// Create a read/write list (Arrays.asList returns a read-only list)
List<String> resources = new ArrayList<>(Arrays.asList("1", "2", "3"));
System.out.printf("Initial state = %s%n", resources);
Collections.shuffle(resources);
System.out.printf("Permuted List = %s%n", resources);
Iterator<String> iterator = resources.iterator();
if (iterator.hasNext()) {
    String resource = iterator.next();
    // do something
    iterator.remove();
    System.out.printf("After remove = %s%n", resources);
}
Output:
Initial state = [1, 2, 3]
Permuted List = [3, 1, 2]
After remove = [1, 2]
NB: This approach makes sense in your case as you have a small list, please note that if you have a big list and you intend to retrieve only a small part of it, you should consider using a Random to get randomly the index of the next element (using nextInt(int bound) with list.size() as parameter) to get (using get(int index)) and remove (using remove(int index)) instead of using Collections.shuffle(List<?> list) as it would cause an overhead.
ArrayList wouldn't work because I need to assign the color(value) to
  the resource(key)
Yes it can work if you use a List of a wrapper class that will contain both, your color and your resource (for example AbstractMap.SimpleImmutableEntry or simply a custom class). It is good enough as you don't seem to need to retrieve the color by resource. If you do, you could simply have a Map with resource as key and color as value and use new ArrayList<>(map.keySet()) to initialize your list of resources, then you will be able to apply what is proposed previously in this answer.