You can always ask the owners of the property if they would be willing to accept you without any type of security deposit/money down, however I highly doubt anyone would unless you have absolutely excellent credit - and even then I doubt it. The fact that you have absolutely no money saved to be used as a security deposit - probably won't give the owners of the properties you are applying at a feel warm feeling inside....
My advice would be to save at least enough for one month's security before looking for a rental. If between the two of you, you are still unable to do that - I would reconsider renting together, or look for a much lower priced unit.
Hope that helps!
Maybe you can make a case on one of those.
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