I think I am gonna use ''cooking over charcoal''. I am translating an old text in which the poet is talking about his hunting trip and how he cooks the meat over charcoal.Unless you're throwing the meat directly on the charcoal and bypassing the grill, I wouldn't say that. Try this:
Bob is grilling meat over charcoal. (Although it's a slightly odd sentence, but the "over charcoal" is correct.)
Bob is grilling steaks over charcoal.
Bob is grilling steaks, hamburgers and hotdogs over charcoal.
"On" implies contact. That's why we say "grilling over charcoal", not "on charcoal".That's unusually literal of you, Copyright. Would you similarly reject 'I'm cooking on gas' or 'I'm cooking it on the fire'?