if i may suggest so as to ignore that puny ass island...
4 example, as Japan, i already have all of china and their allies after a grueling 4 3/4 year long campaign, and USA, Phillies have declared war on me.
after i took over India (not hard at all with total 100 divs

), my fleet of nearly 120 ships of all kinds (8 aircraft carriers, like 20 CVL's, many battleships, cruisers, DD's, etc.) began invasions of the islands high on Rare materials and oil (very vital for japan) when a freak landing in Okinawa by 6-8philipiness divs captured the island. after trying to bomb them (strat bomb, logistical bomb, ground attack, interd, to no effect)i went for the bomb the convoy plan, but after 2 months of siege the supplies just kept getting past my massive fleet like they werent there, and yes, i did set them to convoy raiding. my airplanes were also very unsuccessful in killing convoys.
so i just said "to hell with that shithole island" and went straight for their island, took it in a little over two weeks, and left a small garrison to protect it.
now, no new supplies are reaching them (they have no bases to send supplies from), but i cant annex them either due to them having Okinawa which has 1 VP.
the whole point of this is to tell you to just bypass it. if its a vital island, do everything in your power to get another place from where to launch further invasions.
failing all that, you could nuke them.