Requiring a copy of the lease is standard practice for lending on investment properties, assuming someone is already renting it. 

I tried to do this about a year ago with a local Credit Union that had just started mortgage lending.

They would be able to explain it best and the process in which they lend money and repayment terms.

The property will be paid with by residential lending products and personal money, but how is the business part of this plan be established (i.e., creating a legal contract for rent/finding tenants)? 

The problem is it will have to be an all cash deal at first since nobody will lend on an incomplete property, but there is currently a loan on the property being sold.

I'm currently looking to purchase my first rental property and I'm not able to obtain conventional lending from a bank or credit union.Does anyone know how financing for a rental/cash flowing property works different from fix and flip funding?

Any lending referrals?

Rockwell Institute is the best as far as I am concerned.

My company lends in MI and I’m happy to help if they continue to give you a hard time. 

Pretty far out of my territory here in the southwest to help on the actual growing side, but if you ever need someone to run things past to poke holes/lend ideas, I'm here!