I was there on a rainy day last week and, while these may seem common sense, I'll mention them anyway:
- Comfortable and waterproof rain coat with a hood, slightly oversized, if necessary (I had to wear mine over my hoodie because it was also cold)
- Poncho to go over everything, including backpacks, which the raincoat will probably not cover (also useful for Tiana's)
- Extra pair of shoes (or two if you don't have access to a dryer at your hotel)
- Decent quality umbrella for each person
- PLENTY of extra socks and pants since shoes, socks, and pants will likely get wet even with raincoats, ponchos, and umbrellas
- Get a locker, probably a large one, and keep extra shoes/socks/pants in there so that if it rains early and dries up later you can swap out for dry ones
- Waterproof cover for the stroller, if you're using one
- Quality, sealable waterproof bags of varying sizes (Ziploc for smaller things but also wet/dry bags that you can likely find cheap online). This is for everything from phones/electronics to dry socks you might want to use later or wet clothes to go in if it dries up later in the day and you change.
When it's raining heavily, I like to spend time in the stores in Downtown Disney or especially checking out the hotels (GC and DLH).
Disneyland Hotel has a LOT of history and artwork on the walls to take in. I can spend hours in there even when it's not raining. Don't forget to go up to the second floor and wander around the halls, especially where the convention rooms are, as there is a ton of great artwork to see up there.
Lastly, embrace it. There's nothing you can do to change the weather and, if you can't change the dates, you can either go into negative and be miserable or accepting of the situation with a focus on the positives. I'll take a rainy few days in Disneyland over a dry, sunny day at work any time. Have fun!