Now I look it up, Collins claims that cove probably derives from the Romany kova, meaning “thing, person”. I never would have guessed such a chappish word to be Romany in origin, but I like the generous latitude of meaning it implies.
Of course, the similarity of meaning to covey (a small group of people, by extension from a small number of grouse) is entirely accidental; one of those glancing blows of apparent meaning you get in a jackdaw language such as English.
Every time I see something like that I am reminded that the English ended up with Shakespeare as poet of the nation; verbose, eclectic, eccentric, syntactically obscure, coining more than the Royal Mint, and madly, intemperately punning.
Puns, let us not forget, only work if you have a lot of semantic variance spread over a small lexical space. Cove seems to be Romany, while covey comes from old French. Languages with fewer borrowed words obviously tend to have fewer opportunities for puns.
One upshot of this that pleases me: we should be looking forward to a whole new set of puns emerging based, particularly, on the increasingly visible Indian languages.
Until we do, keep taking the tablas.