A friend is interested in conveying the sense of "don't rock the boat", but in Latin. Is there an equivalent saying in Latin, or a phrase which would convey the correct meaning?
There's a Latin maxim that means exactly that! Quieta non movere (or, more fully, Quieta non movere et mota quietare—that is, "Don't move things that are at rest, and put at rest things that move").
I don't know whether this maxim comes from Roman times or later, but it's been around for a while; in a 1763 letter to Horace Mann advising him about a move to Naples he was considering, Horace Walpole wrote
I do not know what to advise about Naples. You know I always repeat my father's maxim, "Quieta non movere." Besides, should you like it? After so many years, would you care to tap a new world, a new set of acquaintance?