I had this happen as well recently, as Japan. Although in my case, they only started with their tributary nonsense the minute I grabbed a korean province that bordered them directly. Funny thing was that they first declared war to make me tributary - about a week after I got that province - and only after I won that war (I even got war reparations from them), they thought to ask nicely if I want to be their tributary. I found that rather amusing.
Luckily I am able to hold them off almost indefinitely - while they waste time and deplete their manpower on sieging my several korean fortresses, I sink anything of theirs that dares to leave port, and periodically distract them with random hit&run sieges on Beijing or other coastal forts. That causes them to abandon their sieges and rush their army stacks back, thus giving more time for their war exhaustion to tick up, and their manpower to tick down.