If you somehow control multiple copies of Dionus, each permanent you control will have that many instances of the granted ability. These abilities are not redundant. For example, if you control two copies of Dionus and one becomes tapped during your turn, each of its granted abilities will trigger. When those abilities resolve, each one will untap that Dionus (if it's tapped at the time) and will put a +1/+1 counter on it regardless of whether it's tapped or untapped.