f(x)= b * sin (x - a) + c
This is the core function of this idea I had while thinking about stability. Even if it doesn't make it into the game I liked it very much and would at least ask if it would be possible to mod things like this later on.
So here we go:

What we see here is the sinus curve f(x) = 3 * sin(x) + 1.5
We have a base line, which is drawn in red and which is set by the factor 1,5 in the equation above. This factor is the basic stability your leader starts with. As you can see it does not divide the sinus curve into 2 equal parts but to a larger positive part, and a smaller negative one.
The Y-Axis is the stability value (which is about 4.25 in this curve's maximum), the X-Axis is the time in days (scale should be varied and the scale used in this example is just to explain you the idea behind this).
So what does this all mean now? The idea behind this is to get rid of the typical spend money to keep your stabillity up and to avoid arbitrary penalties for the player which can be really annoying some times and which you absolutely cannot avoid.
The suggested system now is being altered completely by the rulers stats, advisor stats and mainly bonusses or malusses given by events. The main part of each reigning period will be the events and their outcomes. A very capable ruler could change the base line (the red line) either up (bad) or down (good).
Positive events can only happen in the time window labelled as 1 (blue) and negative ones only at the time window labelled as 2 (red). In order to make this work the event pool has to be reworked, giving each event a minimum/maximum stability to fire.
From the equation f(x) = 3 * sin(x) + 1.5 the only changeable variable is the 1.5 which basically is your new stability. This variable moves your entire curve either up or down. The given sinus curve shows how it looks on a very capable ruler with only a small time window when negative events can fire (red 2). In short: +1.5 is the bonus from your ruler.
Now every event fires under certain circumstances. The new event system has to link the events possible to your current stability. In old EU3 only the frequency changed during low stability times (maybe there were some special events for extreme situations).
For example: The hated "comet sighted" even can only fire when the stability variable is below 0. In this case we are at 1.5 so the event cannot fire or should at least be linked with a Mtth which makes the chances of occuring very very small during a prospering period. Note that this event is just an example.
Events should always let the player decide either to gain stability or gain economical bonusses. Of course some purely negative choices should remain as well. Every decision made changes the variable up or down bit by bit.
Example:
"My lord an earthquake devasted our province. What shall we do?" (fires regardless your stability level as it is an earthquake!!)
1) Send as much help as possible (effects: lose lots of money, gain positive stability)
2) We don't have time or money for this (effects: gain negative stability)
Now our ruler died. A new ruler who is less capable than his father sits on the throne. The curve might change like this:

As you can see the curve now is divided into 2 equal parts allowed positive and negative events to happen in equal amounts the base line is higher. Now the player has to care even more for his decisions from events or hire good advisors to compensate the lack of leadership.
I am aware of the fact that this might be a big change, but after all it's just one equation with all events linked to it. I am not familar with coding but I don't think this should be hard to add. Just the balance issue would take some more time but in the end I think you'd gain a better system of handling stability.
At the end I fear that my English is not good enough to explain everything like I had it in mind. But I hope it opens some new thoughts and discussions about it here. I'd be happy to see a feature like this in a EU style game.
This is the core function of this idea I had while thinking about stability. Even if it doesn't make it into the game I liked it very much and would at least ask if it would be possible to mod things like this later on.
So here we go:

What we see here is the sinus curve f(x) = 3 * sin(x) + 1.5
We have a base line, which is drawn in red and which is set by the factor 1,5 in the equation above. This factor is the basic stability your leader starts with. As you can see it does not divide the sinus curve into 2 equal parts but to a larger positive part, and a smaller negative one.
The Y-Axis is the stability value (which is about 4.25 in this curve's maximum), the X-Axis is the time in days (scale should be varied and the scale used in this example is just to explain you the idea behind this).
So what does this all mean now? The idea behind this is to get rid of the typical spend money to keep your stabillity up and to avoid arbitrary penalties for the player which can be really annoying some times and which you absolutely cannot avoid.
The suggested system now is being altered completely by the rulers stats, advisor stats and mainly bonusses or malusses given by events. The main part of each reigning period will be the events and their outcomes. A very capable ruler could change the base line (the red line) either up (bad) or down (good).
Positive events can only happen in the time window labelled as 1 (blue) and negative ones only at the time window labelled as 2 (red). In order to make this work the event pool has to be reworked, giving each event a minimum/maximum stability to fire.
From the equation f(x) = 3 * sin(x) + 1.5 the only changeable variable is the 1.5 which basically is your new stability. This variable moves your entire curve either up or down. The given sinus curve shows how it looks on a very capable ruler with only a small time window when negative events can fire (red 2). In short: +1.5 is the bonus from your ruler.
Now every event fires under certain circumstances. The new event system has to link the events possible to your current stability. In old EU3 only the frequency changed during low stability times (maybe there were some special events for extreme situations).
For example: The hated "comet sighted" even can only fire when the stability variable is below 0. In this case we are at 1.5 so the event cannot fire or should at least be linked with a Mtth which makes the chances of occuring very very small during a prospering period. Note that this event is just an example.
Events should always let the player decide either to gain stability or gain economical bonusses. Of course some purely negative choices should remain as well. Every decision made changes the variable up or down bit by bit.
Example:
"My lord an earthquake devasted our province. What shall we do?" (fires regardless your stability level as it is an earthquake!!)
1) Send as much help as possible (effects: lose lots of money, gain positive stability)
2) We don't have time or money for this (effects: gain negative stability)
Now our ruler died. A new ruler who is less capable than his father sits on the throne. The curve might change like this:

As you can see the curve now is divided into 2 equal parts allowed positive and negative events to happen in equal amounts the base line is higher. Now the player has to care even more for his decisions from events or hire good advisors to compensate the lack of leadership.
I am aware of the fact that this might be a big change, but after all it's just one equation with all events linked to it. I am not familar with coding but I don't think this should be hard to add. Just the balance issue would take some more time but in the end I think you'd gain a better system of handling stability.
At the end I fear that my English is not good enough to explain everything like I had it in mind. But I hope it opens some new thoughts and discussions about it here. I'd be happy to see a feature like this in a EU style game.