I know they have them at CTI, at least they had them a coupe of years ago. I saw them used there in 2012.
Look at the activities page for CTI. What are the people doing at the first picture on the left right next to the water activities section? Looks like a stand up paddle board to me. You can even see the Bayside restaurant in the background.
I have a suggestion if you want to know for certain. Use the Couples contact page and ask. You should get a friendly reply in your email inbox in a few days.
CSA had paddles boards and we had never done it before. Friends that were with us started doing it in the morning and they were hooked. We gave it a try and really enjoyed it. We saw tons of star fish and other little fish. The highlight was a big sting ray that was swimming around and we were right on top of it! Too cool. I'm not sure what resorts have the paddle boards, but I know CSA does and we loved them.