A point of divergence two hundred years before Christ's birth would certainly prevent Christianity or Islam from forming due to the butterfly effect in the first place.
The other possibilities are "Confucianism" became different. Remind that "Confucianism" we know today is a huge mix of many philosophies thrived in Waring State period .
As I mentioned before (ancient) Legalism should be the best alternative, but the interesting thing is its concept of people's nature being evil (性惡說) rather than good, came from a branch of ancient Confucianism - Xun Zi (荀子)
However the idea of Mandate of Heaven (天命) is way ancient than any of these philosophies, probably going back to Shang Dynasty or even further. But it is also different from what we know today. The original concept probably came from ancestral worshiping, as the ruler himself is the religious figure head when alive, and ascend into divine-hood status after death, so it's a blood tie from generation to generation.
Later when feudal society evolved and required more and more complex succession law, it absorbed concepts of primogeniture right of crown authority, to ensure the next ruler's right. Somewhat like the later European version of divine right of kingship, without a monotheism god, but series ancient divines of previous kings act as invisible guiding force, they came from heaven, return to heaven, and they are one with heaven.
However during the warring state, rulers were often overthrown, and in political reality that often it's the one who had the ability rather than blood tie actually won in the end, and sometimes even the ruler himself became only a figure head, and the true political power came from the second ladder - Shi (士). However they are not like later Shi consists mostly scholars, but warriors, minor notabilities, anyone who can wield political power peaceful or not (think of samurai in Japan). So a more "democratic" view of rulers emerges, and they seek some convenient back doors in philosophy for their moral high ground. The main stream of Confucianism at that time support this idea, by arguing that if everyone's nature is good since birth, there is no mistake to become rulers if you are able to rise yourself up to Saints. The current ruler should transfer the crown authority to the best Saint in his realm. It essentially said people are granted with the right of rebellion if the ruler doesn't have his virtue (天下惟有德者居之).
But you can imagine this became fairly unpopular among rulers whom favorite centralized monarchy and kingdoms merged. (Like Qin kingdom). Thus more practical approach like Xun Zi appeared and branched out from Confucianism, and finally became ancient Legalism (先秦法家). They didn't deny the subjects' right to rebel. Even reenforced it using a completely reversed concept - people's nature is bad, to explain why everyone is like a ticking bomb, so the ruler has the right to use any mean necessary.
Unfortunately, Qin Dynasty didn't last in OTL. It's successor Han Dynasty didn't choose Legalism, and at first not even Confucianism (waring state style). It chose Taoism (also waring state style, not the type we know today). People are neither good nor bad, and they can govern themselves, the heaven/universe always find a way to maintain statue quo. This is obviously fairly popular for feudal government type if it's at peace. Han Empire were almost like reverse back to a more feudal-like, less centralized alliances type Empire.
Turning point came after the Rebellion of Seven States (七國之亂 154 BC), which nearly reverted the Han Empire back to waring states. The next emperor - Liu Che - mostly known in history as Han Wu Di (漢武帝) - Emperor Wu of Han. He faced the political reality, tried a different approach - Disposed every philosophy, but Confucianism (罷黜百家, 獨尊儒術) at 134 BC (At the time he was still a young emperor at the age of 22) after his grandmother Empress Dou (竇太后) died at 135 BC, who was the true political leader in court and major supporter of ancient Taoism.
But his "Confucianism" is no longer Waring State style. The revived Confucianism proposed by scholar Dong Zhong Shu (董仲舒) has a new concept called Interactions between Heaven and Man (天人感應). It continues the convenient back door of right to rebellion, but modified it in a way saying that the ruler may not be a saint all the time. The heaven doesn't just punished the ruler out right by giving subjects the right to rebel and overthrow him. The heaven "interact" with the ruler by giving signs like nature disasters (天災) or minor revolts (人禍). The ruler can issue an edict of self criticism (罪己詔) to subjects and given a second chance to correct his behaviors (many chances if necessary). This "balanced" approach preserves the Confucius concept of people/subjects are good in nature, and also gives a moral high ground for rulers to save his face and maintain rules. The succession of blood tie no longer need to go through bloody civil wars, like the ruler is given a restricted driver's license. It can be revoked in theory, but in practice it just stay as it is if nothing goes wrong.
So the next POD after Qin Dynasty I believe would be at this point. Han Wu Di only wished to have a political philosophy to keep the empire united without bloodshed due to his young succession. Revived Confucianism is not the only option IMO. In fact it's nearly unrecognizable compare to waring statue style. Late there was a controversy about the the true nature of Confucianism called modern and ancient texts controversy (今古文之爭), last for many centuries (ancient texts were discovered hidden in Confucius' decadence residence).
I think there is a big difference between the political power balance game in ancient China Han Empire and Late Rome Empire. Although both seek the same to unite an empire. In my knowledge Rome Emperors (like Constantine the Great) adopted Christianity for the same practical need as Han Wu Di.
Rome Emperors may not be blood related, and Rome Empire emerges from a Republic previously, so they find certain "force" beyond the realm of mortals to establish a crown authority appeal. The Han Dynasty emerged from overthrown previous Dynasty and essentially cut off the theoretical blood line from the common ancestor of the mystical First Emperor - Yellow Emperor (黃帝). However the first Han Emperor was just a commoner before gaining the throne, and he continued using blood tie for succession. People generally still believed the power of ancestral spirit of previous ruler gives current ruler authority. So in order to resolve this contradiction, Han Wu Di found OTL revived Confucianism appealing.
P.S. This is also the reason why every first emperor has to either come up with a legend of his birth, usually involved his mother impregnated by a divine spirit (Most of the time the Chinese dragon, or some ancient giants), so he got heaven's blessing through other means than his not divined father, or somehow trace his lineage to another emperors in history.
IF somehow during the time of crisis another revived Confucianism can maintain people's believe of ancestral authority with certain ancient branches of Confucianism closer to Legalism philosophy, it should provide compatibility later for various Abrahamic religions to take root (Still, somehow need to reduce the influence of Buddism and Taoism later, perhaps Zoroastrianism can be a bridge much earlier than OTL to form a different version of Manihaeism in China).