What does panegoric mean? Yes, it’s panegoric and not panegyric. The word is given in my module with the meaning “medicine that allays pain”, but I can’t find any reference. Is it correct?
Paregoric, handwritten, is easily misread as panegoric because r in some hands looks like n. You can see this, for example, in this online transcription of medical records,[DOC format] in which paregoric appears ten times and panegoric three times.
This misspelling has been imitated. It has made its way into peoples’ minds, as evidenced by various publications. Not just the popular or banal:
But also the literary and scholarly:
It is very likely that this misspelling has found its way into your module.
Incidentally, paregoric does not mean “medicine that allays pain”, at least not in a general sense. It means a particular mixture of opium, anise oil, benzoic acid, camphor, glycerin, alcohol, and water, originally compounded to soothe the cough of an asthmatic. Paregoric has other uses, notably the control of diarrhea. (See: “paregoric” entry at Wikipedia.)
Also, paregoric should not be confused with panegyric, which is a sort of eulogy. It is even possible that the resemblance between the two words might have contributed to some misspellings of paregoric as panegoric.
The correct term is paregoric. It's of Greek origin and its meaning is the one given in your question. There is a definition at Etymonline.