Honestly I think most of them do give out the birthday cupcakes (they are vanilla with mickey mouse edible confetti!) If price is a consideration first - go to the menus at allears.net and find a place you'd like to celebrate - what is your favorite?
For sit down meals from MK you might enjoy Liberty Tree Tavern - its no longer a character meal, but it has an all you can eat, served family style,
from MK you could take Disney transportation - boat over to Wilderness Lodge for the Whispering Canyon - its a fun, down home place - used to have a lot of silly, fun antics, but its toned down quite a bit so I wouldnt know what to expect!
Polynesian has kona Cafe and Ohana -
all of these places we've been given a special cupcake when celebrating dd bday (or mom's - we've gone quite a few different times)
Epcot is one of my favorite places to eat at -
we ate at Coral Reef and LeCellier
both fantastic meals
(Coral reef, bad picture I know but I see it wasnt the standard cupcake!_
from Boma: This place really went all out in decorating the standard cupcake!
I know you cant guarantee a free cupcake - so I have always ordered a special dessert for our occassions as well...
just make sure when you make the adr you tell them you are celebrating your birthday, and when you check in, I'd mention it again also!!