It's a smaller loan sand having some difficulty finding a lender.

How difficult is it to keep it occupied?

Overall it’s not that difficult. I

I am having some difficulty understanding this concept, could you explain this to me? 

How difficult is this to set up?

The downside of working as 1099 or for yourself is exactly what you're experiencing, difficulties providing enough documentation on your income.

I am having difficulty discerning whether I need to be patient and wait longer or if I just haven’t exhausted all the potential resources.

You can also put it in the lease - "the fridge is yours to use, but you are responsible for paying for repairs, or I am removing it before you move in"Not buying a fridge might result in difficulty getting the place rented, which is a larger issue than buying a fridge in my opinion. 

Are there any difficulties getting delayed financing with 1099 income?

The difficulty is that at different points throughout the partnership, 1 party may be contributing more cash/property management/renovation labor /finding the deal as each persons role wouldn't necessarily be strictly confined, i.e. one party will not exclusively be for downpayment/renovation cost, one party for property management, one party for renovation.