FrequentFlyer, as your profile says you reside in the BFS area, i presume should you urgently need to make your way to Sunny West Yorkshire, you would use the Flybe route. this is the info from their system regarding ID.
Domestic/Republic of Ireland travel
All passengers, adults, children and infants, travelling to the Republic of Ireland must have a form of ID which proves their nationality / citizenship for immigration purposes.
- A valid passport
- An expired passport (can be used on domestic flights for up to two years after expiry)
- Valid photographic EU or Swiss national identity card
- Valid photographic driving licence
- Valid armed forces identity card
- Valid police warrant card/badge
- Valid airport employees security identity pass
- A child on parent’ s passport is an acceptable form of ID
- CitizenCard
- Valid photographic firearm certificate
- Valid Government-issued identity card
- SMART card
- Electoral identity card
- NUS cards photographic (National Union of Students)
- Photographic University/College ID card
- Company ID cards of Nationally recognised companies (photographic)
- Council issued bus pass (Senior Citizens only)
- Pension book (as only acceptable form of non-photographic identification)
- Young Scot Card
I trust that there would be something in the list that would cover you (includind EXPIRED PASSPORTS!)