I've had a problem with the autopilot, mostly with add-on aircraft.  After ascent, it levels off to whatever altitude I've selected, but it can't stay there.  It adjusts trim too far down, then is readjusts trim too far up, and it goes back and forth, up a few degrees, down a few degrees, never able to stabilize.  It's annoying because after spending the time to climb to altitude, a flight is basically ruined by this incredible annoyance (unless I want to hand fly the altitude for 6 hours, not something I find very entertaining)

Does anyone else have this problem or know how to fix it?

Yeh i sometimes get this problem as well, and if you leave it then it will fall a few thousand feet until it levels the pitch...so just set it all manually to level it then auto pilot will carry on.

But some addon aircraft just have problem autopilots.

There are several quite well known addons (and I'm not gonna mention them) where I guess the (very talented)designers decided to do their own fdes, which are terrible. Shame because if a beautiful plane doesn't fly right it's just a dog unless you can change the fde.

No fde should have a wildly oscillating autopilot and certainly not more than a few tens of feet at most. Biggest problems come with the turboprops because M$ didn't design an effective autopilot with autothrottle. Some have been done (inc by me) but it's more or less impossible to get a perfect one.

Pistons and jets shouldn't be a problem though because it's always possible to modify a suitable default fde.

I had the same problem with the Falcon. It would oscillate as much as 1000 fpm up and down. A reinstall of the aircraft took care of it. Don't know why but it worked.

set the base climb rate at 100, increase for ac-type. 747 can do around 2000, fighter jets as high as 3500 for initial.

it won't go much faster up if set above 3000 fpm anyway, there you have the 'vertical limit' stick trick for (set to 80-90 degree up on attitude indicator)

It's easy to forget: Autopilot is an aid, not a magician.

Try doing Mach 1.5 on manual and making a slight adjustment to the altitude via your joystick. Watch the altimeter. You'll be dealing with an adjustment of hundreds of feet, not a few, purely because of the speed you're doing. It's no easier for the autopilot.

Some aircraft have badly set-up configurations for auto-pilot use - no question. However in the majority of cases, problems such as those described in this thread are experienced because simply too much is expected of the autopilot.

As a simple guideline, if you want to achieve a course of 90 degrees with a climb rate of 1,000 feet per minute, put the aircraft roughly on that course and using that climb rate before you engage the autopilot. Don't expect it to perform like slew and magicly line you up without some oscillation. In terms of oscillation at cruise altitude, darkhorse has already provided the solution: slow down. Let the autopilot establish itself then speed up.

In some aircraft you'll get away without doing all this, but don't always expect it to be so.