Before Japan became a centralized state (The Shoguns still were fighting each other), how were Japanese-Chinese relations?

I'm not sure if you mean alliances between China and the shogunates that existed before the Warring States period (Kamakura, Ashikaga) or between China and the feudal lords (daimyo) that ruled the provinces in that era. In either case, yes there were!... Kind of. Japanese-Chinese relations in pre-Modern times were always a bit on and off. I don't know that much about the Senguku period in itself, but I can talk a bit about how the thing were between the Chinese and Japanese courts between the 15th-16th centuries.

Before the Onin war, the Ashikagas tried to establish trade between the shogunal court and Ming China, but in the Main Land they weren't particularly eager to agree to receive envoys, as there were lots of troubles with Japanese pirates (wako). The Ming Emperors had the rule of not doing trade with vassals, and the shogun had to fight with some other clans for the right to declare himself "king of Japan" in the eyes of the Chinese, since he wasn't the Emperor. And who deserved that honour wasn't as clear as it might appear; the Ouchi clan, who would take complete control of the tribute missions to China for some years in the 16th century, and some others had to be subdued. Ahikaga Yoshimitsu managed to secure the trade with the court by returning some of the prisoners the pirates had captured, and declaring himself subject of the Chinese Emperor (We're still talking 1403 here). He made use of the Japanese Imperial family in his missions, and declared himself of the same level as theirs. This of course wasn't that well received by the Japanese nobility, but in doing so, Ashikaga had secured not only the Chinese trade with Japan, but his own monopoly on it. After the Ashikaga lost their preeminence, however, the missions to Ming China were disputed between the Ouchi and the Hosokawa clans. The problem is, as I've mentioned that China wasn't willing to talk with anyone other than the legitimate ruler of Japan, which, at the time, wasn't that easy to pinpoint. So both families sent impostor envoys, taking charge of the missions in different years. Sadly, the increase of piracy, the lack of understanding, and the growing mistrust between the Chinese court and the envoys of the"King of Japan" led to these efforts being stopped in the year 1551.

So in these particular cases there's lots of backstabbing and a desire to find legitimacy for their own status in the country through their relations with China.

Sources: "Japanese-Korean and Japanese-Chinese Relations in the Sixteenth Century" in The East Asian War, 1592-1598: International Relations, Violence and Memory, James B. Lewis, ed.

"Japan and East Asia" by Kozo Yamamura in Cambridge History of Japan vol. 3 Medieval Japan.