Ehrich, J. F., & Meuter, R. F. (2009). Acquiring an Artificial Logographic Orthography The Beneficial Effects of a Logographic L1 Background and Bilinguality. Journal of Cross-Cultural Psychology, 40(5), 711-745.
Also, Charles Perfetti and Ying Liu have worked on acquisition of chinese writing.
There have been several studies that have used a miniature version of Japanese (Mini-Nihongo). An example is below but you will find several papers with Mueller at the first author that use this language in training studies. I believe these studies used auditory presentation so if your focus is the written system, this may not be entirely helpful but if you need just a small selection of nouns, verbs, etc. this may be a good start.
Jutta L Mueller, Masako Hirotani and Angela D Friederici. 2007. ERP evidence for different strategies in the processing of case markers in native speakers and non-native learners. BMC Neuroscience 2007, 8:18 doi:10.1186/1471-2202-8-18