oops. that's a problem. that down payment check had to be sourced and seasoned with bank statements from 2 months prior. any undocumented deposits are going to be a problem. You can't call it a gift, it wasn't. It's not the lender being nitpicky, those are the guidelines for the loan.
Have your cosigner write a good letter of explanation for those deposits, with exact amounts and dates explained, and hope that other compensating factors are strong enough and there aren't any other large unexplained deposits.
remember, any money in the transaction has to be sourced (all pages of bank statements) from 2 months prior to the contract date.
I'm going to guess that cash rent is not on a tax return and probably no lease with tenant. Sometimes I've seen where a family member lived in an in-law apartment and helped out with expenses.