Hm, honestly I'm not sure if any country could beat Japan. No European country can at least, since all were involved in some way with the Napoleonic wars, which ended 200 years ago this year. No American nations either, as none besides the US is old enough.
A POD that butterflies the Napoleonic Wars or involves older New World states (whether through earlier colonization or surviving indigenous kingdoms) is fine.
Maybe I can stumble toward a list of qualifications. One is being geographically isolated or at least on the margins: it's easier for an island or peninsular nation, or one protected by mountains or desert, to stay at peace than one that's on all the invasion routes. The country in question would have to be strong enough to deter would-be conquerors, or else the peace would end the way it did for the Moriori or Ryukyu Kingdom. And they would have to be uninterested in territorial expansion, whether out of a desire for social stasis, fear of what might happen if they try to play in the big leagues, or something entirely different.
I'm thinking that a surviving Inca empire, once it reached its natural borders and worked out a method of avoiding succession wars, might have followed the Tokugawa model. Alternatively, a mountain Asian country might pull it off - maybe one of the Himalayan Buddhist kingdoms could stay out of its neighbors' quarrels.