I am pretty sure the short answer to your question is - no. Flights within Ireland are all Aer Arann and Ryanair.

Indeed the only internal flight from KIR is to Dublin.

But it seems that Knock International NOC does not offer internal flights at the moment!

You could fly Dublin to Sligo SXL or Dublin to Galway GWY if you fly KIR to DUB or even Cork ORK to Galway if they are relatively close to where you need to go/from?

Some airport websites that may be of help:

http://www.kerryairport.ie/

http://www.galwayairport.com/

http://www.sligoairport.com/

http://www.dublinairport.com/

http://www.irelandwestairport.com/ Knock

And those domestic airlines:

http://www.ryanair.com/

http://www.aerarann.ie/

The only way you would have been able to fly was kerry to Dublin and Dublin to Knock. However as someone else pointed out the carrier that went from Knock to Dublin has ceased flights and by the time you would have done all this you would have been there by bus or train. Other than hiring a car you could go by bus www.buseireann.ie or by train www.irishrail.ie

The rail journey is not a direct route though you have to go kerry to portarlington and portarlington to Ballyhaunis/Claremorris/Castlebar/Ballina/Westport depending on your destination. The bus is the more direct route.

Have fun