We are straying a bit off topic here. I don't think any country has been stable for a "few" hundred years. A few is 3. This is before the US was founded.
I would say a stable country is one which has had a legit democracy for 70 or so years and doesn't share a border with a non-democratic / non-legit-democratic state. These two points suggests its unlikely to have a revolution or be invaded any time soon.
Of course, if you look at the UK governments track record with IT.. you wouldn't trust it. I would say the same with the US, especially in concern with data security.
I think I could argue that England has been pretty stable since at least the end of the Civil War - which is 360 years ago. A lot of the institutions that form part of the current UK go back an awful lot further than that.
I'll reject your democratic requirement out of hand, as democracies haven't proven particularly stable. There was that trial-run in Athens which lasted 501 years (508 - 7 BCE, with interruptions). Other than a few small/outlying instances (most notably the Althing in Iceland, it didn't re-emerge until the short-lived Corsican Republic (1755), and of course, the United States (1776).
Japan (660 BCE) and China (221 BCE) have both had feudal / bureaucratic governments exhibiting very high levels of stability. While dynasties and eras are marked, the overall states persisted largely intact.
I would say a stable country is one which has had a legit democracy for 70 or so years and doesn't share a border with a non-democratic / non-legit-democratic state. These two points suggests its unlikely to have a revolution or be invaded any time soon.
Of course, if you look at the UK governments track record with IT.. you wouldn't trust it. I would say the same with the US, especially in concern with data security.