Heavier bridge, less break angle over the bridge (adjust tailpiece so it is higher above the head).

Smakula Fretted Instruments sells skin heads.

I'd say first just lower the head tension and see where that gets you. I like my bluegrass banjos up at like 91, but seem to like my ITMs down at like 85-86ish on the drum dial. This make a much larger difference than the head type, in my opinion.

Head type does makes a difference, but I can't say myself I'd want to mess with a real skin head changing tension based on the weather. Remo makes a fiberskin type head that's supposed to sound similar to skin, but is mylar and doesn't have weather issues. Those get REALLY dark, maybe further than you want to go.

It looks like a goodtime artisan comes with a top frosted head. A renaissance (sort of cloudy translucent) or white suede or black suede head will knock the edge off the brightness. It seems the renaissance is the standard for ITM, but I'm beginning to like the suede heads as well.

Looks like a goodtime artisan comes with a presto type tailpiece. If it's adjustable, set it so it's further away from the surface of the head, almost to a straight line from the bridge to the edge of the banjo. This makes a large difference as well, and won't require swapping parts.

If you want to play with a real skin head, Smakula Fretted Instruments sells them (and usually has good prices on regular heads as well).

I like Renaissance heads for this very reason. Takes just enough brightness out of it. I also use Scorpion bridges with a wider top

John Balch for hide heads hidebanjoheads.com/shop
I like 'suede' style plastic heads (available from smakula fretted instruments), but hide can sound amazing.

Thanks everyone. It does have a renaissance head, so I will take some of the suggestions here, to see how it goes.
I had no idea how much fun the 4 string Irish can be. I play guitar with a Celtic group, and one of the guys had one. I’d quit playing Scruggs a while back, but having a banjo in my hands again is a huge joy!

You can setup your banjo however you want, but none of the suggestions here are what is the desired sound in Irish traditional music. Regardless of what head you're using 85-86 only has the banjo running at about 25% of its capability. This will lead to a quiet, plunky, muddy sound that will not be heard in a session. It will also make you work 3 times as hard as a properly setup banjo.

A Deering Artisan is not a bright banjo. Do you have any sessions near you with any banjo players? Where are you located?

I go through this process often with newer people to the music and learning the banjo in the US. There is a very specific setup and sound that we desire in trad, and it often shocks people when I setup their banjo. I usually have to make it a 2 or 3 step process as they adjust. But once you play a well setup cracking banjo you will never go back.

I’m in Northern Idaho, and play with a group who play many different instruments. We have a frailing banjo, my tenor, couple of mandolins, a tenor guitar, my guitar, a hammer dulcimer and four fiddles. I would not call us a real session, since we practice at the local library. Our most experienced player says that the banjos need to be damped down, so I have a sock in it.
I don’t know how far away a real session is, perhaps Spokane WA, or maybe Boise ID.
We are all friends in my group, we laugh, play music, and support one mando player who has cancer. It’s the perfect spot for me.

Making music with friends is what it's all about, glad you're enjoying it. Here are some suggestions to "dampen" the sound of the banjo. Although, I don't know how the banjo will be heard over the hammer dulcimer and 4 fiddles if it is too quite. I assume you are picking melody on it, in which case you would want to be able to be heard along with the other melody instruments.

1. Reduce the tension on the Ren head, you will hear the tone and volume drop off as you loosen it. A drum dial is a handy tool to record what tension you are at and allow to experiment with different tension and easily return to your favorite.

2. A different pick, try a lighter and softer nylon, or if you're still too loud a felt pick will definitely make you quieter.

3. Nylon strings. I would not know what strings to recommend but I am sure people have used nylon in GDAE tuning and a search here might be able to help.

4. Pick further away from the bridge, closer to the neck.

5. Use a heavier bridge

6, Change the tailpiece out for an Elite tailpiece.

Hope some of this helps, keep us posted.

If it is open back, just shove a cloth between the rods and the head. Vary the thickness of the cloth by folding etc to get different results. Easy, noninvasive damping .

I did this for an Irish group class once so I could hear my instructor better.