Probably between 5 to 10 million, I'm just guessing. Disease from these contacts will keep the numbers down to a certain degree, but it seems like the land is there for the taking. Particularly once the potato gets introduced, but buckwheat and other crops should grow well too. Warfare will be another thing keeping the population down, since this sudden population growth with more efficient agriculture will tax Maori social structures, especially if the Chinese are selling them guns. Earlier and more brutal Musket Wars, basically.
By the late 19th century? This is ludicrously high.
OTL population in 1840, before European colonisation had really begun, was only 100,000 at a maximum - and it was about the same when Cook arrived in 1769, so it seems that there was population stasis at about the 100,000 level. You could argue that the introduction of a variety of crops and new agricultural practices would support a much larger population than the staple crops of the previous centuries, but a 5,000% increase in population in 60 years is simply not physically possible.
And that's before you look into the reasons for OTL Maori population decline. These were:
1) The spread of diseases like influenza, TB, etc. from other continents. This isn't going to change vastly in the absence of Pakeha colonisation, because you're still assuming heavy trade and minor migration with China and other parts of Asia. These populations carried the same diseases, and would still communicate them. Even in the case of early Columbian America, where inter-continental contact was relatively minor at first, Old World diseases still killed a vast proportion of the population before the Conquistadors gave way to actual settling populations.
2) Venereal diseases. If there are Chinese people visiting NZ, they are going to have sex with locals. Some of them will have STDs and these will be spread into the local population, as in OTL. Fertility will therefore be reduced, potentially below replacement level.
3) Muskets. This is a very minor cause of death in 19th century Aotearoa. However, it may be reduced if the Chinese don't trade weapons for whatever they want from NZ. Not statistically significant, though.
So we've established that there's still going to be a steep population decline
however the Maori are introduced to the rest of the world. I would even go further and say that the recovery of the Maori population in 1880-1900 was principally due to the efforts of Pakeha immigrant doctors working to improve public health and prevent what they saw as the extinction of the Maori (which they saw as a great shame). Without European colonisation, this would not happen to anything like the same extent, and the Maori would have to wait for natural immunity to build up. Chinese medical practices would probably only transfer in a major way if they colonised NZ, and even then they were arguably inferior to Western methods.
So all in all, I'd say the Maori population in the late 19th century would be anywhere between 20,000 and 50,000, and certainly nowhere in the millions.