Free rotation
What about temporarily giving players a random skin if they already own a champion in the free rotation but have no skins for him/her/it?
This would allow us to try skins in-game before buying them, and should also increase the overall purchases of skins (it's a known marketing device: you give a normally non-free service for free for a limited time, and when it's over there's an increased chance that people will pay in order to keep it).