The new tenants are supposed to move in tomorrow and have paid first months rent with no lease signed.  

@Eric TanJust based on the limited info, I would structure a Lease with an Option.

They are on new leases with 9 months to go.

This will be especially useful if they decide later to ask permission for another family member to be added to the lease (sibling, nephew, elderly parent, etc) and you have already set the standard that everyone will be need to have a background check.

Perhaps when the lease is up for renewal and the child is 18 years old you could then do a screening but it may not make sense to if he or she is good tenant at that point and continuing to share a room with the leaseholder.

Depending on the bank, some will account for the cash flow within the first year if you can prove to them the length of your lease with a tenant and how much cash flow is obtained each month.

Then the buyer would agree to let the tenants continue to live there granted they sign a lease and start paying the going monthly rent, which depending on the condition of the house could be about $2000 - $2400 a month.

I've inherited two leases, but they don't start until September (the house is empty now).

I suppose I could borrow those funds from a family member and then pay them back with the owner-financing proceeds over the next year, but then I lose the benefit of owner-financing (i.e. the interest).Not sure the buyer can wait until my listing agreement expires, as their lease expires in May, a month before my agreement.

I have a tenant that has been in my unit for two years and just signed another 1 year lease extension.