The conventional wisdom is that families with smaller children start in Animator's Palate (APLAPLA), those with older children start in Parrot Cay (PLAPLAP), and adults traveling without children start in Lumière's (LAPLAPL). This is by no means a hard and fast rule, though. While we (adults with no kids) have always had LAPLAPL, we've been seated with families with small children before, as well as at a table which was all adults.
You can try to change it once on board. On embarkation day, there will be a time a place set up to meet with the dining manager to request changes. They'll try to accomodate you, but there are no guarantees.
I personally, do not think one rotation is necessarily better than the others, so I just take what I get and go from there.