Who are some private lenders that don't have strict mortgage requirements like most banks?

I'm a self-employed contractor that earns checks and cash.

RP-Funding told me that they don't want to see any cash deposits from the last 2 months when applying for a mortgage...

Are there any private lenders that don't have so many upfront requirements?

I'm looking for a lender who will check my credit, take my downpayment, and approve me. Do those still exist?

I understand they might require a higher down payment cost + higher interest rates, but I'd be fine with that.

Any help/info/advice is appreciated. Thanks!