” the Carteret Islands are only a short distance from Bougainville where no such sea level rise has been reported. Moreover, the area is only 500km from some very serious recent volcanic activity at Rabaul and form part of an active volcanic chain through the Solomon Islands. … The islands lie in one of the most complex tectonic areas of the earth. They sit next to a plate convergence zone at the boundary of the Pacific Plate, Indo-Australian Plate, and South Bismark Plate on a subduction zone next to the New Hebrides Trench (Bougainville Trench), where the earth’s crust is disappearing.” http://ianmott.blogspot.com/2007/03/rising-sea-levels-or-just-sinking.html
California’s draining the San Joaquin valley has lowered the land dramatically, including islands in the river like Twitchell Island. http://www.msnbc.msn.com/id/26096152/
In the Mississippi Delta “the wetlands’ erosion in Terrebonne and Lafourche Parishes caused by natural subsidence, the rerouting of the Mississippi River and, some say, global warming.”
http://www.nytimes.com/2006/06/19/us/19road.html
“Venice had been sinking since the very beginning. The Alps are partly to blame. The weight of this mountain range is bearing down on all of northern Italy, slowly driving it into the sea. But even more damaging to Venice is what lies below. CHARLES E. MCCLENNEN: Underneath Venice is a salt marsh. Venice is sitting on several layers. The uppermost and thinnest are the lagoon sediments, fairly muddy and, in part, salt marshes, and that’s what Venice was built on. Below that is nearly a mile thick of river sediments. Those sediments are slowly compacting.
NARRATOR: In effect, Venice is sitting on a giant sponge filled with water. As the weight of Venice pushes down on the sediments, it squeezes some of the water out, and the sponge gets thinner. http://www.pbs.org/wgbh/nova/transcripts/2914_venice.html

The disappearance of Krakatoa was a different kind of phenomenon where a volcano collapsed enough to let in sea water which created a giant explosion that blew most of the remaining island into the sky, and generated the loudest sound historically reported

I’ll guess there are other sinking islands whose misfortune can be only partly blamed on rising sea levels. Barrier islands like the Outer Banks of NC constantly shift and disappear but you probably would not call getting your land washed away a sinking if the underlying base remains at the same altitude.

Living in touch with the sea has always been hazardous.

And don’t fear, the few islands actually sinking doesn’t affect the truth or falsity of your conspiracy theory.