Jennifer,
With a good rain poncho, perhaps an umbrella, and a bit of a “singing in the rain” attitude, any of the parks can be great to visit on rainy days. Rain usually means the crowds will be lighter, and many of the attractions and most of the shows are housed inside buildings or at least under cover. Besides, many times the rain doesn’t last for long, especially in the summer.
If you asked me to pick one park, and you did, I would have to say Disney’s Hollywood Studio (DHS). Why? Well, because almost all of the attractions and shows at DHS are sheltered, and the park is more compact, so you don’t have to walk so far between the attractions.
On the other end of the spectrum, I think the Animal Kingdom has the fewest attractions under cover, but still could be great fun in the rain -- especially if you bring the right attitude and some raingear along as well. ;-)
If rain is in the forecast, and you have a stroller, be sure to bring a plastic sheet or poncho to cover it as well.