Dear Liz:
I'm the family cruise editor here and this message board has had a lot of discussion in the past about swim diapers. The cruise lines usually post a sign saying that anyone in diapers is not allowed in the pool. However, there isn't always someone there checking that everyone adheres to the policy. Some parents have found swim diapers that are part of the bathing suits and have used them without a problem.
As for Sting Ray City, you will be on a small boat. While your 22 month old could stay on the boat with one of the adults while you're in the water, it might be tough keeping the toddler occupied the whole time. ALso, chances are it will be hot just sitting on the boat too. I have a toddler and that would not be for him -- however, you know your own children! The teen will love it and they 7 year may or may not, depending on if they get afraid of the sting rays once you're in the water.
I hope this is helpful. What line are you cruising on? A few have babysitting (RCI, Celebrity) which you may consider using while you're on the Sting Ray City tour.
Smooth sailing,
Luisa Frey Gaynor