Removing tuition, you should be able to survive on 100,000 yen a month. I say "survive" as there will be little left over for fun stuff.
Here is tuition for one school in Tokyo
Duration Registration Tuition Total
4 weeks \21,000 \74,800 \95,800
6 weeks \21,000 \112,200 \133,200
8 weeks \21,000 \149,600 \170,600
12 weeks \21,000 \179,000 \200,000
SJI-Japanese Language Course - Learn Japanese in Tokyo