My husband and I (both 62) will be making our first trip to Ireland in Sept. Hope to fly into Shannon from London, then spend time in Dingle. Can we do this easily without renting a car?
You can fly Ryanair from London Stansted to Shannon and take Buseireann buses from there to Dingle. Or you can fly Ryanair from London Stansted to Kerry and take Buseireann buses from there to Dingle. Bus service is limited on Sundays.
Supplementing Tim's excellent (as always) answer, this site will give you an idea of the extent of rail service in Ireland http://www.irishrail.ie/home/and this one the extent of bus service http://www.buseireann.ie/
I forgot one flight option: Aer Lingus from London Heathrow to Shannon.
Read the book "around Ireland with a fridge" by Tony Hawks!
Roger