Fannie和Freddie需要的租金收入证明，一是以前税表里的Sch E Part I，

二是现在的lease agreement。你现在的情况应该属于“Documenting Rental Income From Property Other Than the Subject Property”，即你现在要贷的款，需要用到另外这个你已经拥有的出租房的收入。如果是这样的话，Fannie Mae的规定是：

"When the borrower owns property – other than the subject property – that is rented, the lender must document the monthly gross (and net) rental income with the borrower' s most recent signed federal income tax return that includes Schedule E. Copies of the current lease agreement(s) may be substituted if the borrower can document a qualifying exception. See Partial or No Rental History on Tax Returns below."

如上可见，Fannie Mae并没有针对month-to-month lease的歧视。如果你现在的贷款经纪认为month-to-month lease贷不到款的话，那应该是他/她所代表的银行自己的规定。建议不要作假，换个房贷经纪就好了。