According to this FAQ for online check-in
, "Where a passenger is unable to avail of Online Check-in by reason only of not being the holder of either a valid passport or a National Identity Card, issued by the government of an EU/EEA country, any Airport Check-In fee paid will be refunded upon application."
Here is the address to write to for refunds:
Ryanair Refunds Dept
Ryanair Head Office
Co Dublin, IRELAND
You can also fax refund requests to Ireland +353 1 812 2130
You must include the following: Confirmation Number (e.g. ABC123), Full Flight Details - date/routes, Passenger Names
They will reply to the email address associated with your original itinerary. Refunds are made directly to the card used for booking.
Another method to avoid the fee is to go for online check-in when making your booking, but arrive at the airport far enough in advance
to check-in at the counter. It's unlikely they will attempt to extract the fee from you then when they take note that you are a non-EU citizen. Even if they do, you can always follow up using the above information to request a refund.