Well Dennerle, all I can say is that the term "stability" is relative. If you mean overall price movement, meaning more "stable" currencies move less, then I would not want a stable market, because we need movement to make money. I think a more appropriate definition for "stability" would be: price that moves according to some sort of order... (ie. steady trends, not many whipsaws, obeying fibonacci, etc.)
I have noticed that the forex market has a great deal of stability... yes, there are erratic times (after news releases, after Bernanke or Geithner open their mouths, etc...) This market happens to be very excitable.. But when the market is clear of news or any other geo-political events, then there is a very nice order to it, and a lot of money can be made.
If you look at the big picture,
currency 
values do not change that much over the course of a trading session.. only 1 to 2 cents per day.. It's the
leverage 
that is provided to forex traders which make small movements equal large gains (or losses). So if you can understand how to manage this
leverage 
along with your risk, then you are way ahead of the game..
If you have a hard time obeying
risk management 
rules, then maybe you want to try your hand at using a forex robot trader to do your trading for you.
I hope this helps.
...good trades,
Bot