So less than 10% that you are bringing to the table and you want the world? Of course you want to keep the payments as low as possible but you are essentially asking for close to 100% financing.
Do you have a plan? Do you have experience dealing with other rental units in your business?
I see some major concerns that lenders will have looking at it from a cash flow and backing perspective. I hope you have some good credit or you are going to have problems getting what you are asking for.
If you have good credit though you should go an unsecured route to come up with what you need. From a hard money perspective though you need to change your perspective. You are asking for a long term loan on something that you don't own and trying to back it with financials that you do not own. You must qualify on your own and have the backing even if that fails for a lender to take you seriously. This is why I ask what your relationship is with the owners because there are ways to be creative.
Overall from the sounds of it you are a start up, have no proof of experience on paper, trying to obtain funds on someone else's income. You have a lot of hurdles to jump over.