Shrunky Dinks are a toy and activity kit consisting of sheets of polystyrene which can be cut with standard household scissors.
In "Quagmire's Baby", Peter compares the cheapness of Quagmire's $50 ham radio to being an even bigger rip-off than Shrunky Dinks. A cutaway gag then plays of a boy being disappointed by realizing the dinks in the box have already been shrunk, to which his father wishes him a "happy Birthmas".