We were there at the end of May and our Daughter who turned four while there had a few favourites, which were the following in the order, listed:
Dumbo the Flying Elephant
Casey Jr Train
It’s a small world
Le pays des Contes de Fees
Mad Hatter's Tea Cups
Pinocchio’s Fantastic Journey
Le Carrousel de Lancelot
Slinky Dog ZigZag Spin
My favourites were Casey Jr and Dumbo but then I don’t like anything big, fast or scary.
My youngest DD is three. When we were there a couple of weeks ago she loved small world, casey junior, POTC, pinocchio, snow white (be aware there is a lot of scary witch in this ride) peter pan, buzz lightyear, parachute drop and slinky dog.
You can also add the flying carpets and (possibly) the Cars ride at the Studios. Plus the Riverboat, Keel Boats and Autopia too.
Animagique, Playhouse Disney and Stitch at the Studios will all be OK too.
The Stunt Show and the Tram Ride may be OK (depending on whether the 3 year old likes loud noise or not).
POTC is a bit of a puzzler - the dark queue for the ride (along with older kids making scary noises) scared my DS who was 5 at the time. The actual ride itself probably wasn't that scary (but then he doesn't mind looking at skeletons - he was more worried about getting a few drips of water on him!).
Start with the gentler rides first, then build up gradually is my advice.