Huh? Why would you accept peace? Never accept peace. An AI that trickles its units towards you is providing an additional resource - XP. Just let it trickle the units and harvest the XP. In addition, you can generally also acquire workers via steal, and get gold on the side via pillaging. None of this activity generates warmonger status.
Even more fun - you can use your horse units and Privateers to raid their trade routes. Those yield nice rewards and is kind of fun.
So your suggestion for a warmongering neighbor is to live in a constant state of war with them sometimes from the beginning of civilization all the way until future tech?
And you don't see this as a problem with how diplomacy works?