Hope I'm not late here. As other have suggested, Pakistan will be the first obvious allies, but I think it will also be one of the shortest live alliance they have. Because China-Pakistan relationship is tonally based on their antagonism towards India. They have very very little shared common cultural values. But their relationship in the near terms will be good, long term not so much.
In the long term I believe Asia will go back to the sino-centric order where China, Korea, Japan and Vietnam will be in the same sphere. Obviously this is like 30-50 years in the future. As much as those nations all hate each other, but they have very similar cultural foundation, they have all be heavily sinocized for centuries, they share similar beliefs in Confucianism, Buddhism, Taoism and the order of the world. And as early as 19th century they were still part of the China sphere. But during the last 200 years as China got weaken they broke apart, but I still think deep down they are still the same. And as China gets stronger they will again go back to that order.
In the old days, China's number one geopolitical foes are the nomadic hoards coming from the north, the Mongols, the Manchus etc... I don't think Mongolian plain will ever have another chance to threat China's existence. So I the long term of history, I think the rise of industrialization is actually extremely beneficial to the Chinese civilization. However I think sooner or later Russia and China will became rivals. They didn't usually have problem with each other until recently during the Qing dynasty, because Russia itself was expanding towards the West and before that it was somewhat un-populated. But they are not destined to go to war with each other, because the peace between Qing and Tzar Russia hold for 2 centuries as long as both nation can defend each other, and in the age of nuclear ICBM, this can be easily accomplished. But I still think if you have to pick their biggest threat will come form the north in far future.
As for India, there will be no war with each other. Simply because of Himalayas the biggest and best natural barrier between those two civilization. And they really have absolutely NOTHING to gain by attacking each other, both lands are extremely populated. And both nation have hard time feeding and governing it's own people, let along govern each other's conquered population, their culture is as different to each other as difference spices.
For Africa they may establish some kind of client state relationship based on trade and mutual economic interest. And with very remote chance of spreading Chinese culture there, but it is not impossible. Because I strongly think Africa needs a strong does of Confucianism to get some self discipline. And their existing culture is relatively weak.
For Latin American, it will not be any client state relationship with China, because USA will still be there. I think eventually US will retreat from Asia, but it can still control it is own backyard easy. So China's relationship with them will not change, it will be a purely economic exchange.
As for Europe, this is hardest to say, because Europe have no freaking idea what it wants for itself right now. On one hand they are still suffering from PTSD from WW2, so they are trying to do whatever it takes to be politically correct to stay peaceful. But on the other hand they are facing problem of demographic crisis as population shrink, facing population pressure from Middle East. But if you look at Europe not so long ago, they were the most bloodthirsty nations on earth, so I don't know, maybe they will go back to that tradition, pick up arms again and blow each other up, blow up the Middle East. Or can try to maintain status quo or even integrate even more closer. But whatever it is, they will have equal relationship with China, they won't see China as a threat as US do, maybe they will even work closer with China simply out of necessity.
As for Middle East, only bad thing will happen. I think their mindset is still stuck in Europe's 14 century. Still really need to get over their obsession with Allah to have any chance to modernize and compete with rest of the world. I hate to say it, in the long term they have the worst outlook of all, they have this huge population growth, ever depleting of oil reserve, and no development of their internal economy such as manufacturing or service or agriculture, and they are still obsessed as hell with their relationship with God which dominates every single fabric of their life and think everything revolves around that. As for China, it will be a purely trade relationship with very little cultural or political exchange/alliance. Because both civilization think they got the answer to humanity's problem, and best of all, they don't hate each other, but also not willing to fully accept each other. This will not end up well for Middle East overall, they will implode and maybe take down Europe with it, but China is still far away, so they should be able to isolate themselves from that.
For North American, AKA USA and Canada. US will have a hard time dealing with their declined influence all around the world. One thing for sure, they will abandon this mindset that they are the 500lb elephant in the room and can get the whole world to bend to their will. They will once again learn the limit of their power, and how they will take this is the biggest challenge to humanity. Because as US economy shrinks it is influence will shrink as well, but one thing for sure, their military will be the last sector to shrink. It is very possible for them to became a police state like North Korea where the only functioning institution left is the military and vest government bureaucracy. So it is very dangerous for a nation trying to hold down to what they have purely base on military power, if it is not carefully we might even start WW3 and blow up half of humanity and set back our progress back for 200 years. But I think that will not happen, US will be able to deal with their relatively decline somewhat peacefully. But still no matter how much US power declines it will still have a very strong position. Because it will always have the best damn geopolitical map in the world, above them is Canada, aka America Jr. Below them is Mexico and if needed they can really seal off the border if necessary, and Mexico will still be a lot weaker than US for a long time to come, and so is South America. So American will maintain it is sphere in it is own continent, if not through culture/economic means, but surely with purely military dominance. As for their relationship with China, it will be peaceful overall, but nothing significant.
Sorry for the long post, it got away from me.
