1. 12 months bank statments/saving statements showing a saving of atleast that much.
2. Say you are willing to move in whenever the landlord would like.
3 A letter from an accountant stating how much you earned last year in non-taxable income. Would be considered proof of income, secondly you could have them write on this letter that they believe that you could support this liability.

Be upfront about it if they ask, and if they still reject you ask to set-up a meeting with the landlords and put your own spin on yourself, rather than the warped presentation of a real-estate agent.

P.S I used to be in property management before I changed to finance broking, if they think your hiding something they will not even give you a chance.