Shel Silverstein and Dennis Lee (who is often quite good) are not what you would call "nonsense" verse writers. They almost always make perfect sense and their poems present understandable arguments and sentences, even if they are fanciful or funny. "Nonsense" verse usually refers to poems that are not just silly, but ultimately either senseless or utilizing mostly made-up words. So I would think you might be interested in any number of children's poets writing today. Kenn Nesbitt, J Patrick Lewis, Joshua Seigal, Roger Stevens, Jack Prelutsky, and many, many others. And looking to the past, my favorite would be AA Milne (he has two fine poetry collections that are, in my opinion, essential classics). Some Dr. Seuss (e.g., One fish two fish"), and Lewis Carrol (of course).