Students form teams of 5-10 (the more students in a group, the more challenging it will be). Works best if the desks are facing each other in some way, like a rectangle or circle.
Use janken to decide which student will begin. Student 1 turns to the child on their left and asks, "What do you want for your birthday?" Student 2 replies, "I want [answer]." Student 2 turns to Student 3, "What do you want for your birthday?" Student 3 answers, "I want [Student 2's answer] and [Student 3's answer]." Student 3 turns to Student 4 and so on until Student 1 is reciting what everyone in the group wants for their birthday.
Of course the students can say whatever they want, though decide for yourself the degree of katakana-eigo you will allow.