The parents firstly may not want to give permission as they do not want the children to go alone to the cinema, Secondly, they might have the feeling that the children may be tired after spending the whole day at school and hence need rest which is very important for their health. They might not want the children to miss out on their homework and studies of that particular day. The children according to their view must learn to be responsible with one's studies rather than skipping those for cinema. Lastly, the parents might want to go along with children for the cinema, but that particular day may not be suitable for them. That might be the reason why the parents are not giving permission for cinema on that day.
What children can do is that , they can discuss with their parents how much they wish to go for the cinema and why they are not being permitted. Knowing the reasons from the parents' part would definitely help. Throwing tantrums or being fussy would never help. The children have to assure their parents that they would not skip their studies, but will finish everything on time, will reach back home on time without wandering and that they would obey whatever their decision is. The children can request the parents to come along as they could spend time together too.
When the parents are convinced about the childrens' good intentions I am sure they would give permission right away.