The lender would consider that a gift from your friend, independent of whatever type of agreement you come up w/.  

Using an FHA means this method would not be the way to go.Private Money - These are people that are willing to lend you money based upon whatever agreement you can both agree on.

What you do need is a clear written agreement on when/how funding will occur, what rate of return, default, etc.

Well what does the agreement say exactly.

I just found this buried in the 28 page agreement.

Yes, put the property under contract and assign the contract using an assignment agreement to a buyer.

Since you are working with a buyers agent, and I assume s/he is assisting with some of the sourcing of deals, you might consider this situation a learning experience as what to expect when you get into competitive buying situations.Depending on the price of property it might be advantageous to reach an agreement in advance with your buyers agent to pay them a fixed fee or % of the agreed to price when a similar situation arises.

At this scale, you need legal assistance, this can be done with a master lease arrangement and you can also secure your interest as a future advanced note/obligation agreement to cover additional money invested on repairs.

Do you do background and credit screenings on your applicants, also did you purchase a rental agreement specific to NY or did you modify a free one?  

If you are doing it with a friend its a multi-member LLC  not a single member LLC (unless you just want to do a JV agreement) so your operating agreement should spell everything out.With that being said there are definitely advantages to having an LLC such as financing and sometimes tax related advantages but  if you are not raising money its may not vital to have an LLC though your own situation may vary.