Ryanair accept either a passport or a photocard driving licence for travel between the UK and Ireland and (as far as UK citizens are concerned) absolutely nothing else:
http://www.ryanair.com/site/EN/faqs.php?sect=p id&quest=photoid
Easyjet don't fly to or from either Manchester or Dublin airports.
Luxair fly the route but their flights aren't suitable for day trips (because of both timings and fares).
According to the Dublin airport website, the only other airline flying the route is Aer Lingus. (They offer flight prices from �1 + taxes & charges, each way, between Manchester and Dublin). They accept passports or 'official photo-ID'. This would almost certainly include a driving licence but anything else would need to be be checked in advance:
http://www.aerlingus.com/cgi-bin/obel01im1/Ser vices/passports_visa.jsp?BV_SessionID=@@@@2130 224866.1174246343@@@@&BV_EngineID=cccgaddkhfhh kkmcefecfigdffgdfkj.0&P_OID=-8076&Category=3#i rluk
Chris