The biggest tire you can get away with without having it pinch was the Bridgestone Battlax BT-016 150/16 but I think they don't produce them anymore. I sold my Ninja 250 but I can recommend that tire 100%.
In my opinion having a larger tire is not the problem with the ninja feeling stable, it just has to do with the weight of the bike. You just have to get use to the feeling of being blown around a bit.
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