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. For safety, parents should remove the needle from a hypodermic syringe. Always remove the cap on the end of all syringes before injecting the medication into the child's mouth. The cap can pop off in the child's mouth and create a choking hazard. FDA is working with manufacturers to eliminate the safety hazards posed by the caps.