What are Antihistamines doing in a baby?
This song most likely refers to an off-label (and usually inappropriate) use for certain antihistamines like Benadryl. They are sometimes used by parents to sedate their children, functioning through the exact physiological mechanisms @Chris describes.  Parents use it inappropriately as a means of behavioral control for active or upset children to make them more docile or sleepy, such as for airplane rides, etc.  It's not recommended by most pediatricians, because even though adverse (bad) side effects are usually rare, it is an actual medication with another primary mechanism of action having effects on many body functions, not a medication designed as a sedative.