Several things.
Firstly, if everything is adjusted correctly, a large component of your discomfort is psychological. Secondly, you will never be perfectly comfortable.
Set your seat at a comfortable height. Pretty much, that’s as high as you can put it without feeling like you’re stretching for the pedals. Only lower it if you’re doing MUni or “skills” (freestyle or trials for example) in which case you won’t be sitting down for long periods anyway.
Set your seat at a comfortable angle. With a conventional seatpost, sliding the seat forwards slightly raises its nose, and many people find this a bit more comfortable.
Now, wear padded cycle shorts - and (really) don’t wear underwear underneath them. Cycle shorts have the seams and elastic in the right place. Underwear has the seams and elastic in the wrong place for unicycling.
I wear padded skin-tight shorts under padded cycling longs.
Now, get lots of miles in. Don’t stop too often. Get a rhythm going.
I find shorter cranks and a faster cadence somehow make it less painful.
You can alleviate your suffering by occasionally standing on the pedals, or by partly supporting your weight with the heel of your hand on the front of the seat (or on the handle).
With a standard Viscount saddle and no handle, at my peak, I could do 60+ minutes without excessive discomfort, and I occasionally did two hours. However, after that first burst, I tend to stop every 15 minutes or so - even more often towards the end of a long ride.
Overcoming the pain is part of the challenge. No one said it was easy.