Odds of finding short-term renter in winter months?

Hello BP! I have a dilemma on my hands.

My father is in the middle of a divorce. They're selling their house, which is huge, old, and needs many repairs. I do not anticipate a smooth sale. His credit is in bad shape, so I will finance the purchase of a new home for him. He is my PM and business partner. 

A family friend recently passed, and her home is being sold for what's owed (which is $15k-$18k below market). It's the right size, right neighborhood, right place, and the worst timing. I could finance the purchase no problem, but we're afraid of holding onto a house for 3-6 months, maybe more, with no renter in it while he tries to find a new place. We live in NE Ohio; I think finding a short-term renter is tricky even during prime moving months. We could get through a month or 2, but any more than that and we'd be walking a financial tightrope. But I also hate the thought of buying in the spring when prices are at their max. 

There were other things we wanted to accomplish while prepping his current primary as well: refi one of our other rentals, build a nest egg to prep for the purchase of the new place and his moving expenses, and pay down some debt. I need a new car before winter hits, and I wanted to downgrade to a much less expensive car to cut my monthly payment in at least half to help with these plans and time the credit inquiries right. This really throws a wrench in our plans. 

Any advice? TIA!