I found that making a colony in taiwan let me become a tributary of Ming even after they rivaled me. If you want to never be rivaled at all, you're best off not taking the Shogunate until most of the Daimyo are gone, since all of those individual armies are what add up to make Japan powerful enough to rival.
Alternatively you can quite readily beat Ming as Japan if you hit when their mandate is the 30s from passing a reform. If you want an easy way to begin blobbing into Korea and weaken Ming, make your first war a trade war (easily wiping Ming's fleets and eating all the armies they try to ship out) while declaring a simultaneous war on Korea before finishing the war vs. Ming. Ideally Ming is left with low manpower/funds, lots of WE, a short truce, and you've taken a few forts in Korea to bleed them out in the next war. With low mandate and no manpower/low merc limit Ming is completely toast.