Are you asking which LCDs themselves support Chinese characters, or which Handled supports CHinese characters? If it is the latter, than you can easily find many PDAs in the Chinese language, including an iPod like video/music player and power PDA runnung CE .net...
I have been studying Chinese in China for 2 years and have found several problems with Chinese on any kind of pda. First of all, can the pda (hp/c or ppc or palm) use Chinese fonts. The second question is, is there software out there for that pda with that Chinese font. There are different kinds of fonts i.e. big 5, etc and not all software/pda combinations will allow them to work.
According to the literature, the ce OS was designed to be unicode so that should make a ce machine a better choice than a Palm...but it has taken the applications people a long time to get apps out that make use of this feature.
What has been said so far pertains to READING Chinese. If you want to write Chinese, with most ce or palm machines you must find an add-in to the unit. For palm this is usually kjcos (hope I got the name write) and for the ce there are a couple, the one I have heard the best results from is called Monster CE If you are really serious and in need you can get many ppc's (haven't heard of any hp/c's) with a Chinese version of the os installed in the chip itself.
Then of course, you have to pay attention to whether you need simplified or traditional characters...