Susanne:
You may be in for some roadblocks using that strategy. As you mentioned the Co-op Boards can and do make things difficult to work a rental business in their complexes.
Many (but not all) specifically prohibit renting out the units. Some of those that do allow it limits the amount of time the unit can be rented out and charge an addition fee as part of the maintenance fees to have the unit run as a rental.
On the tenant screening side of things the Co-op board and /or management company many want to do their own tenant screening (possibly helpful, definitely slows things down) but they can charge a relatively hefty fee for processing.
Long and short of it is, your strategy CAN WORK, but their are some additional hurdles to clear. Check the Co-Op Bylaws carefully and talk to the Co-Op board.
