I have just turned down three enquiries in 24 hours because the ceremony time had already been booked. There is no doubt that 75% of weddings occur on a Saturday afternoon, around 4:00 pm. The earlier you contact your celebrant, the more likely you are to get your preferred choice of both time and celebrant. I offer a discount for ceremonies that are held on other days of the week, and it can be a great idea to think laterally and consider the possibility of NOT marrying on a Saturday afternoon. I also provide an incentive to hold the ceremony slightly earlier, and holding a day-time party. These can be great fun too! My earliest ever ceremony was held at dawn - I certainly don't endorse this as a great option, but recently officiated at a ceremony at 10:30 am , and this led to a huge outdoor party for family and friends, and in this case, included a large contingent of children.
If you know your ceremony is near a long weekend, Fridays and Sunday can work very well for your guests, and you are more likely to get the celebrant of your choice. This is especially so if you are planning your ceremony with relatively short notice.