Hi Guest!
I'm also a teacher in a private school and I see your point when you talk about the lack of confidence in students. From what I have seen, this seems to be their main problem when practising speaking skills.
What I usually do is pair work and competitions. Teenagers seem motivated when they can be winners... or losers
![Wink [;)]](/emoticons/emotion-5.gif)
I use different tools and approaches to achieve this: videos, discussions, definitions games, students' dictations, picture descriptions, etc. It depends on their age and the English they know. It is useful to encourage and praise them when they speak the foreign language. It makes them confident to speak more next time.
I agree with your point "practice makes perfect", but the bad side is when their other teachers encourage them "not to speak English if you don't know how". I tell them the opposite: "Try, try, try and practise speaking as much as you can". I think it's the only way to improve.
To sum up, I think it's a great idea to offer these Conversational English Lessons, and that many students would need them. Good luck!
These are my ideas but I'm eager to hear what the rest of (more experinced or not) teachers have to say about this.