If staying in a Disney resort, they will give you buttons for everybody to wear. If not, then stop in at City Hall when you arrive, and they'll give them to you. I can only imagine how the CMs will respond when they realize the triplets are there on their birthday (and mom, too).
Make a lunch or dinner reservation, and there would undoubtedly be a fair bit of attention shown there. They usually provide a dessert of some variety (cupcake tends to be the usual), so it would be interested to see what they might do for you, especially if you can make it clear that you're there on the actual birthday itself (most of the buttons you'll see are likely on someone whose birthday is being celebrated but not necessarily on that exact date).
Would also be fun to try to become the family of the day. From what I'm told, you should arrive at the gate about an hour early, "look the part" (Disney-related clothing would probably help) and play nice (i.e., bribe the triplets to get along for a while - ha!). I would bet that having triplets would help attract the appropriate CMs' attention when they're out there looking for the family of the day. If you don't get it, then at least you're near the front of the line and would have an hour or two of pretty short lines to everything before the crowds really roll in.
Happy birthday!