The Point Of Divergence
Mao's "Great Leap Forward" had disatisfied a lot within the Party and the military. Many became disillusioned with Mao's hardline communism, which was rapidly destroying the country in the eyes of these men. Eventually, former Kuomintang General and Korean War veteran Peng Denhuai organized a coup d'etat against Mao Zedong.
On July 1st 1959, a gunman stormed the Lushan Conference, killing Mao and wounding several of his supporters at the conference. Peng, labelling it a "coup by nationalist forces" used this as an excuse to arrest and purge hardline communists within the military and government. Peng later wrote that the plot was in fact inspired by the earlier July 20th plot against Adolf Hitler.
Peng soon was installed as the new leader and followed through with a series of social and economic liberalisations, as well as more friendly relations with the west. During his tenure (1959-1974) he managed to more quickly recover China's stagnation in the 50's.
For the most part the cold war stayed the same. Taiwan was still unsure about reuniting with China. It was still a de jure communist state and it certainly wasn't pro-western. The Sino-Soviet split still occured and Nixon still went to China.
But... The real difference from OTL began to show in the late 80's as China's economy was booming.
The "Twin Jewels Of Asia"
By the 1980's China and Japan were the economic powerhouses of Asia. China and Japan by 1985 ranked 2nd and 3rd in terms of GDP respectively and a rivalry was beginning to form. However, in 1986 Japan's economy was starting to grow at an unsustainable rate. The new Chinese Premier, Cheng Buoxing, the first civilian leader of China after the 1959 coup, saw this fact and decided it would be best to help Japan.
Cheng, who took power in 1986, was seen as a great mediator between the two nations and relations between the two warmed over the late 80's until the establishment of the "Asian Economic Community" or AEC in 1990 between China, Japan, The two Korea's, Taiwan and Vietnam.
Cheng also presided over more social liberalization. Acting to grant more rights to the Chinese people after the Tienanmen Square Protests, he became popular worldwide.