I've had the same problem before -- Boxed, not Steam. Couple of reasons.
Both causes can also been reported to sometimes result in altitude "porpoising," where the aircraft won't settle.
From what you've described, it sounds like this is cause by an issue between the FMC and the GPS directing the autopilot. If the VNAV mode is selected on the FMC, it will take over the altitude target selector and will command a climb or descent to the altitude it intends to be at for the next waypoint.
(One way to deal with this is manually change the altitude of each waypoint in the FMS to the present/desired altitude.)
You'll notice this either when you select VNAV on the FMS, or when selecting NAV on the autopilot (if the FMS is commanding).
It would appear Carenado has treated this issue as a bug which was reportedly addressed in Service Pack 20140129. Some persons report that installing that SP fixes this issue.
The SP is available from the Carenado website -- if you purchased the aircraft from them you can log into an account. If purchased elsewhere, they want some proof of purchase (I don't know what form).
I have not yet installed the patch, because I've only just found out about it and haven't troubled to dig up my purchase information. (And, I simply never use the VNAV mode.)
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Second possible case, as Bert said, is the weight distribution. This really is a very sensitive bird in that respect. I've read that 1900 pilots litterally say this bird is "&@($*-heavy." In the real-world, docs show the center-of-gravity allowed range is about 28 inches from fore to aft. So the loaded cog must be somewhere within a range less than two and one half feet.
This aircraft comes with a tail stand bar to keep it from tipping backwards when bags are loaded before passengers.
Take extra care to balance this aircraft, especially fore-to-aft. And, as Bert wrote, keep the weight away from the aft area.
When comparing the loading stations in the aircraft.cfg to real-world docs (with actual datum info), or even just against the approximate locations of the seats in the model -- it turns out that Carenado "compressed" all the station locations towards the center point.
Using the crew seats as an example, the loaded weight of the pilot and copilot are placed (in FSX) actual many feet behind the location where their seats are shown in the model (or in real-world docs). Similarly the aft baggage compartments (there are two in real-world) are placed well into the passenger section of the cabin.
All the passenger seats similarly have a seat "pitch" much less than the standard 30 inches.
I do not know why Carenado did this, but it certainly could be because of this aircraft's high sensitivity to cog deviation.
Apparently, there was one 1900 crash which led the FAA to revamp some rules about standard/assumed passenger weights. And, this also seems to be one of the aircraft for which some carriers literally weigh each passenger and each bag.
I've done some experimentation with the config file station locations, seeing what it's like when the load stations are in the correct locations. It's even more touchy then (but with well-controlled loading, managable).
So, I've run into the same issue. Take off tends to be fine, initial climb okay. But, when the throttles are pulled back for cruise, the attitude goes quickly bad into a stall. It's got to be flying fast if loaded too far to the rear.
Hope this info helps.