Replacing germanium diodes BZY83C10

The B in BZY stands for silicon (or another semiconductor with about the bandgap of silicon) and the Z for Zener, so I think these are 10 V silicon Zener diodes. Try to find other 10 V silicon Zener diodes with the same or a slightly higher power rating and they should work fine.
 
If you can find a datasheet somewhere (on the internet or in an old databook), you can look up the power rating and try to find another 10 V Zener with the same or a slightly higher power rating. If not, you can try to find one that has about the same size, chances are that it also has the same power rating then.