What does Ryanair do without Sick Bags?
Well how many people get airsick during each flight and how many of those really vomit? And of those, how many actually use the provided sick bags? I'm not familiar with getting air sick but I'm sure there are not a lot people really using these bags. There is also no legal requirement for having sick bags. It is an item for 'additional passenger comfort'. Ryanair probably thought this way and so they saved some more money.

They also don't hand out sick bags when they are encountering chops but I'm sure they will have one for you if you ask them.