One word answer: No.
The only flights from London airports to Cork are as follows:
Aer Lingus, from Heathrow ;
CityJet, from London City (only until 26 July) ;
Ryanair, from Gatwick and Stansted.
The only flights from Luton to the southern Irish Republic are as follows:
Ryanair to Dublin and Kerry ;
VLM to Waterford.
Assuming that you wanted to travel by public transport (rather than hiring a car), if you flew into Waterford you'd need to take a taxi to Waterford bus station and then bus No 40 to Cork:
http://www.buseireann.ie/timetables/1441376699-40.pdf
If you took a flight to Dublin, you'd need to take a bus to Heuston station
http://www.dublinbus.ie/Your-Journey1/Timetables/All-Timetables/74711/
and then a train:
http://www.irishrail.ie/media/01a_dublin-cork_direct_280915.pdf
If you travelled to Kerry Airport, there's a direct bus to Cork:
http://kerryairport.ie/website/wp-content/uploads/2014/04/Kerry-Airport-Bus-Timetable.pdf
or you could travel from Farranfore rail station (which effectively serves the airport, as it's only a 10 minute walk away) by rail:
http://www.irishrail.ie
If I had to choose, I'd either fly to Kerry (and then take the bus) or consider using a different London airport.