Are you sure that your husband requires a passport to travel to Dublin? British citizens don't require a passport to enter the Irish Republic. Airlines do require photo ID; their rules vary but most accept a photo-card driving licence, so your husband might not need a passport.
To try to get a new passport for your husband, you should phone 0870 521 0410 (24 hours per day) to seek an appointment at a passport office. It's normally recommended that you should do this a fortnight in advance but it seems that a few appointment times are kept open for really urgent applications. The information, on the link below, states that you can collect the passport for your husband if you take evidence of his identity and a signed letter of authorisation from him. However, it occurs to me that your husband will also need to sign the application form. I recommend that he collects the form from a post office and completes it, so that you can take it with you.
http://www.passport.gov.uk/general_urgent_with in48hrs.asp
Chris