Consider putting the broken side down (so it looks like a dome on your workbench), and cutting with a hand saw with the saw held horizontally. You should be able to hold it down reasonably easily by placing your palm on it and pushing down.
Cutting horizontally can be difficult, but you might be able to place a block of wood on each side of the shell that are the thickness of the piece you want to cut off. Use these pieces of wood as a guide to keep the saw level.
If it ends up working reasonably well, you may want to make an "official" jig for this, screwing or gluing some blocks of wood together to make it a bit easier. If you want the finished rings to have parallel sides, you will also need a way to make your guide blocks adjustable so that you can cut at a slope since I'd assume that your breaks aren't exactly aligned along the equator of the coconut.