There are 3 fundamental requirements:
- you can speak japanese, or get someone speak for you in japanese
- at least one japanese willing to become your guarantee
- you must show that you have earning to pay for the rent
Then, there is the second case. If you are a working person, your boss may become your guarantee. Of course, if you are doing well job in the company...... or nobody will become your guarantee!
Don't blame if you denied by the house agent. There must be some misunderstandings, or the house agent is a stubborn old man or women. Stubborn old man or women always deny foreigners without any reasons. If you find out that the house estate is the stubborn one, just give up, or you can try persuade and prove how nice are you... it is always tough...
Let the house agent know in advance your are foreigner and tell him/her your history in Japan like how long you have stayed, what is your japanese language proficiency, where are you working, etc. If the house agent willing to continue the talk, then your are succeedd half the way!