I always said "Sir-no", unless I'm singing a Japanese fansong, in which case it's always, well, "Chi-ru-no". I've spoken to a couple RL friends about Touhou, and we've all said "Sir-no". Nobody's corrected us yet, so...
If I had heard the Japanese pronounciation first, I think I'd be saying "Churn-no", which is the closest I'd know to articulate. "Cheer-no" sounds even closer, though.