Hi there... there is no specified time for the waiting period. You should check with management agent how big is the waiting list. The shorter it is-the better for you. Sometimes it could be question of days sometimes years. It all depends on the number of people vacating the parking spots. Some sell apartments, some stop using their car, etc... I know 2 buildings on Sheepshead bay, one has a spot available today, and the other has a long waiting list. Also you might find useful to ask for a spot in the buildings around the one that you choose.
Hope this helped. :)