If you don't care where you stay, nor require a specific type of lodging (you have 5 members in the family and need a two bedroom), you probably wouldn't have too much trouble for a few times during the year, like early Sept and early to mid January, maybe early May. From late Sept to Jan 2 it would be very hard. Summer could be very hard, spring break/easter could be very hard.
Most members plan their vacations from 7-11 months ahead of time.