I don’t have a fun and entertaining way, but I wanted to put in two cents anyway. My husband DMs frequently, and regularly has players miss sessions. Life gets in the way, whatever, no biggie. He always explains players being gone as a story that is told long after it happened - different people remember things slightly differently, sometimes they remember certain important figures being there and sometimes they don’t. They might even argue about it, ten years down the line. To him, every session is just another chapter in a story, told by imperfect people with imperfect memories.

I was in a weekly game for preteen girls and their dads. Our standing rule for missing players was that their character was with the party but had terrible diarrhea and was off in the corner, shamefully pooping the whole time.

It worked for the game’s demographic. Fun and gross and gave everyone a chance to lightly tease the player who missed the last session.

I’m running a game for a discord server and by its nature people will drop in and out. So I wrote it into the overarching plot. Reality is literally coming apart at the seams. Objects and creatures from other worlds have been leaking in. At the same time things have been dissappearing without a trace. Not just stuff either, an entire city just vanished in a flash of green light. A powerful wizard is investigating and needs adventurers to go out and do the grunt work. They’ve been traipsing about the planes trying to find the missing city and some clue as to what is happening.

There’s also a monk who’s working for the wizard. His job is to escort adventurers where they are needed via portals, meaning people will occasionally appear mid-adventure. Sometimes people slip out of reality. They experience it as a few seconds but the real time elapsed varies.

I’m running a mutants and masterminds game that runs 1:1 with real time so a week between sessions is an in game week.

When someone can’t make a session it has been explained away as their character being in the hospital or off on their own mission doing something to help the party with the central narrative or their own side quests. I may have them roll a few things over text, but in general they get something out of it to feel like they have contributed to the story.

You can use a generic excuse that works for the table at large, but ideally you can find one in the character’s backstory somewhere. This just helps tie it all together a little bit, helps maintain better immersion.

Some various excuses are visiting someone, be it friends/family/mentor/whatever, training time, some other responsibility (a cleric might be told by their order to go do whatever), medical issue, extreme bouts of sloth, basically being Batman, paying a debt, taking care of a small solo mission or whatever comes out of your ass that day.

Alcohol poisoning - drank too much the night before and can’t face the day. They’ll catch up later!

If you must have them with the party you could run them in a supportive role and simply buff the party where possible (bless, guidance) and keep them off the front lines.

If the players trust each other enough you could have one of them run the character in a similar way to lighten your load.

Beyond that others have suggested good ideas: shopping, a job from their holy order, helping someone in town are always classics.

You could perhaps have the guard arrest them for something and have a jail break as well 🤣

I actually decide with the players one of 3 methods for missing players after I got sick of trying to come up with ways that they pop in and out every session. A. Your character was assumed present but invisible, you get filled in and were there in character B. Your character ceases to exist, there is no in-story explanation and you’ll need to catch up on the details in character. C. The missing player comes up with a reason for their disappearance and what they were doing

But I’ve also had some fun with it before, One of my players in high school warned me ahead of time that once school started up again they’d not be able to make it until the next break. This resulted in them being possessed by the BBEG and culminated in the party saving them as the break started up again, I then had the perfect excuse of them being partially processed by the defeated BBEG who was taunting them with their past, so when they missed a session it was because of possession or manipulation by said character.

I’ve also heard of people having some on-the-nose solutions like getting whisked away to another dimension to help them defeat an evil villain between sessions or getting lost in a pocket dimension/ethereal plane.