Twice!
2003 and 2008
Although as said we didn't actually win it, but were the highest placed team that hadn't naturally qualified for Europe and England was the highest placed country in Europe.
I recall last game of the season in 2003 - the last game at Maine Road - and it was between us or Middlesbrough and there was only a couple of yellow cards between us.
All through the game hoping no one would get a yellow.
Word spread throughout the ground that a Boro player had received a red card and the ground erupting lol
A strange ending to the game. Disappointing we lost the last game at Maine Road but delighted we had qualified for Europe for the 1st time since 1978 / 79