Stingray Touch is a fun exhibit with a dozen or so stingrays to touch. It is open in the summer (late May to mid September) and included in the standard admission. Stingray Touch is actually outside on a terrace, so it will close when there's bad weather (a little rain shouldn't be a problem, and the exhibit itself is covered, although the path and line for it are not). From Caribbean Reef, take the path to the Oceanarium that's next to the Amazon (the right of the two stairs/elevator paths to the Oceanarium). Continue straight ahead and go right out the doors just before the 3-D movies.
Feeding Stingrays
Feeding stingrays is just available before 11am. Tickets are $5 ($3 for members), and should be purchased at the 4-D theater before you go outside to the stingrays. Kids should be 6 or older. Each cup has around 4 minnows, so ideally I recommend 1-2 people per cup, but you can share a little with larger groups. They'll show you how to hold the minnow low in the water so the stingray can suck it up into its mouth (a stingray's mouth is on the bottom, the openings at the front are gills). You'll need to be a little brave: once you put a minnow in the water, several stingrays are probably going to come over and check it out, and it feels a little weird to have your hand under the swarm. Putting your hand low in the water will help avoid getting splashed by stingrays, and putting it out away from the wall helps the rays swim over you smoothly.
Tips for Stingray Touch
Although I always recommend going to Wild Reef first, Stingray Touch is also a good place to visit early. Stingrays are more active early (they mellow considerably after their afternoon feeding, around 1-2pm). If you want to feed them yourself, you'll need to make it by 11am. Even if you just want to touch the rays, it's helpful to be near people feeding them because you'll get several rays near the edge (at other times, many will swim in the middle where it's hard to reach). Touch the stingrays with a couple of fingers gently on their back or wings. They feel soft and a little slimy.
The pool is surprisingly deep (I have reached my whole arm in and still had stingrays swim underneath), so it's best to go to spots where the floor of the pool is raised, which gets the stingrays to swim higher. It's also helpful to be in the parts of the pool that are not as wide, so the rays are more likely to swim near the walls. On the side of the pool close to the building, there's also a window where you can look in and see the stingrays from the side. The far side has a step to make it easier for younger kids to reach into the pool. The youngest kids may put their stomachs on the wall to reach in, but sitting on the wall is not allowed. Most school-aged kids should be big enough to reach in and touch the stingrays on their own.