In at least one case, they were inaccurate. In 1992, FDA received a report of a child who had been given two tablespoons of acetaminophen rather than two teaspoons because the cup had confusing measurements printed on it. The incident prompted a nationwide recall of medicines with dosage cups. Syringes are convenient for infants who can't drink from a cup. A parent can squirt the medicine in the back of the child's mouth where it's less likely to spill out.
Syringes are also convenient for storing a dose.
The parent can measure it out for a babysitter to use later. Some syringes come with caps to prevent medicine from leaking out. These caps are usually small and are choking hazards. Parents who provide a syringe with a cap to a babysitter for later use should caution the sitter to remove the cap before giving the medicine to the child. The cap should be discarded or placed where the child can't get at it.