Looking for a good 9 day itinerary

Where do you want to start? Does the nine days include the day you arrive, and the day you leave, or do you have a full nine days in between the day you land and the day you leave? It will make a big difference in your itinerary, especially when using public transport because you will lose at least a half day of touring when you have to get on a bus or train to get to the next place. For this reason I would suggest taking Blarney Castle off of your list, it's just a tourist trap, and it's not really close to the towns I would suggest using as a base with such a short amount of time. If you have a full nine days I would suggest using Dublin, Killarney, and Galway as bases to tour from. If you have less than nine full days I would suggest you split your time between Dublin and either Galway or Killarney. The reason I say this is that it's easy to get coach tours from these three places, and there is a lot of variety to pick from. If it were me I would just use Dublin and Galway (my favourite) even if you do have a full nine days to travel. It will just simplify things. Land in Dublin, spend four days there, get the train to Galway spend the rest of your time there, then get the train back to Dublin to fly home. Or do it the other way around and just go straight to Galway.

So you've abandoned the idea of getting a car (per your other post)?
If so, and with such limited time available, then I agree with Anita that you're better off basing yourself in just a couple of places and day tripping from there. November travel means shorter days and the increased likelihood of bad weather, so basing in the city will present you with many more options than trying to venture further afield.
Galway would be a good choice - easy train journey from Dublin and lots to do in the area...then back to Dublin for your last 4 or 5 nights. There are lots of great day trips available from Dublin - Glendalough, the Wicklow Mtns., Powerscourt, Newgrange, etc. Belfast would be doable as a day trip as well.
Blarney Castle would be too much of an outlier to fit comfortably into your itinerary, IMO.
Safe travels.

Anita, we will have at least full 8 days there. I thought about starting off in Galway. Robert, as of right now I am more or less leaning towards just using public transportation. I will have to brush up on my bus travel because when I've been there before it was basically exclusively trains, and walking. I haven't completely ruled out renting a car, but it's not exactly winning the race right now for how I want to get around.

Then I would definitely stick to just Galway and Dublin. I spent four nights in both places and found there was lots to see and do.

Hello,
I was in Ireland in July and I did a tour with Vagabond Irish tours. Felt it was responsibly priced, because I didn't feel good about driving by myself. I really enjoyed it.

My daughter and friend ( both 20 yrs old ) toured with vagabond tours ( Wild West coast 8 day ) in May this year and it was the highlight of their holiday ( which included Wales , Scotland and England as well )