I suspect there was nothing special about MZ2360 diodes and you could just use a 1n4148. That would explain why they are no longer marketed. If you provided a pointer to the schematic, then we could be certain. Info I found saz a forward voltage of 0.63 to 0.71 V @10mA, which is a typical silicon diode.
http://njsemi.com/datasheets/MZ2360 - MZ2361.pdf
http://njsemi.com/datasheets/MZ2360 - MZ2361.pdf
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