In the baby room, there is a diaper changing table where you can change the baby's diaper. Once complete, a dirty diaper will appear on the floor that you can throw away.
Other people also had trouble determining where to change the diaper! Unfortunately, the trash can mini game is confusing because it always shows a dirty diaper as if that's what you are always throwing away. But, the reality is that whatever you are holding is what you throw away. So if you took the baby to the trash can... you actually tried to throw out the baby :P We just ran out of time to make the mini games better :(
Thanks for playing!