There are some other battles held during the day and whatnot. Or you can just call out on the Battlechat to see if anyone wants to have a contest for you. I would not want to have multiple -social- battles on the same day unless they were several hours apart. Anyone can host a battle though so if you want to...go for it!
It is really a function of finding battle coordinators available in that time slot on a regular basis. I will keep my hears open for people interested in organizing one in that time slot.