What's the island top made of? If wood, I'd use Titebond III waterproof wood glue. For large surfaces, use a disposable 3" roller for even and complete distribution. I've used Gorilla Glue also, but it's messier to work with.
I haven't found liquid nails to be worth much except for plywood subflooring installed on floor joists and then the subflooring needs to be screwed down tight.
Bill