I want to travel with Ryainair and/or Easyjet from my hometown to a destination that those companies do serve but not directly from my hometown. Is there a site that can help with these kind of requests (to match arrival and departure hours of different flights of the same airline)?
Low-cost airline transfers are non-protected even if you fly with the same airline on both legs, which is why they typically won't show up in a search. Not only that, you will have to book each leg separately (again, even if they're with the same low-cost airline).
If you search with SkyScanner, tick the option "Non-protected transfers" under "Multi-part booking". This is not checked by default.
I'm not sure where to find this option on other engines or if it even exists.