So one of the fun things about history that I've noticed is a tendency for strong nations to develop long lasting, competitive rivalries with neighboring states.
The Danes had the Swedes
The English had the Franks
America had the USSR
The Romans (and later Byzantines) had the Parthians (and later the Turks)
the Iroquois had the Huron and so on.
Yet when it comes to the various Chinese Empires it doesn't really seem like they had a foreign nation they really competed against or rivaled. Sure there were various wars to conquer/reconquer Vietnam, but it doesn't seem like the long lasting feud where foreign nations really threatened them.
There were the steppe hordes in Mongolia and the surrounding regions, but they were frequently disorganized and couldn't really be called a rival power until they were unified under the likes of Genghis Khan.
I'm not sure just how many time Japan and China went to war, but given their relative resourced I doubt Japan could go on long and sustained campaigns against a unified China, assuming it even wanted to.
Lastly the various states of India would seem to be too concerned with their immediate neighbors to focus on China.
So was there any real "rival" for China, or were they relatively indomitable so long as they were unified?
Well, the China you see today is the result of the merge of many cultures. There was nothing such as China until after WWII but only some dynasties based somewhere on nowadays China's territory. Other than the Mongols, a lot tribes had succeeded in conquering China and later, merged their own lands to the conquered lands, enlarging the territory. Take a look at the map of the seven warring states and three kingdoms era and you will understand. In fact, many "steppe hordes" as you put, were large kingdoms with civilized cultures and religions. Their army were far from being disorganized. The Jurchen, a long time rival of both Mongols and China dynasties, defeated Ming dynasty and created Qing dynasty, was such a kingdom. The Liao, another such "steppe horde", was also dominating Tang dynasty until they was hit by a smooth Mongol.
The closet country to be considered as China's rival is Vietnam. After Han dynasty, Vietnam has always been at war with China, at least for 1000 years with various invasions from China. Again, look at the map of Vietnam from all over the eras and you will see that the northern part of Vietnam rarely changed. It's not because there were no invasion but because the tough resistant of Vietnam against China. The tension is still high even in the current era.
Japan actually never fought against China until 17th but Japan beat China in every war since then. Japan also closed to destroy China in WWII should Russia and Us didnt intervene.
India had never been a rival to China. There was no tension between both countries until the recent years. Also, there was no India. The India you know is formed by merging various kingdoms in India subcontinent...by the British. There were some empires closed to control the whole India but that's it. Their empires had never touched China's territory thus no real disbute.