From: Bremen, Germany
What you need is a german HQ, 3 or 4 bomber units (preferable tac air or at least med bombers).
If you trust the Italian Navy, you can use a corps for an amphib invasion. Once the corps has turned into an amphib unit, this unit can once fire on the target before it invaded. These hits often kill 2 - 3 strength points. You can use your Italian Navy for shore bombardements, but I wouldn't recommend it. They will to often suffer damages while firing.
If you don't trust the navy, use a german para unit to drop into the empty island once the defenders are gone. Shouldn't take more than 2 or 3 turns, but comes with a price (movement of the HQ and air units, and more or less your entire air forces will be chained to this operation).
"You will be dead, so long as you refuse to die" (George MacDonald)