I've done this two ways. These are specifically for students who insist on conversation and start to lose interest in the lesson if I bring up grammar exercises and whatnot
1) Follow the book Compelling Conversations by Eric Roth. It tends to work well with young professional-aged students
2) For older students (35+), my private students have always been pretty serious professionals, so I use current events. I print out two news articles (I use real news but you could print out a graded article from breaking news English) and go from there. Might be a bit tricky with beginner but should be fine with intermediate. Make sure you send them the article before the lesson and ask them to read it. They probably won't but still, you should do it. Not sure how long your lessons are but a 90-minute lesson for me might look something like: 0 -15: Small Talk. Drag this part out. People love talking about themselves. "Oh, you visited your in-laws last week? Where are they from? Do you get a long with them? Tell me about that because In my culture it's common not to...blah blah blah 15 - 30: They read the article aloud, I underline and circle certain words as they go. Once they finish we go back and fix pronounciation and I quiz them on the meaning of some of the words. This should only be for certain words, not every mistake 30-45: Practice the target vocab in the reading (quiz, use it in a sentence, etc.) 45 - 90: discuss the article and use answers to point out just a few small grammar points.
Not sure where you live, but I've found politics to be one of the most enjoyable topics for most students 30 and up. Where I live they don't have many opportunities to share their views, especially with a foreigner, and this really gets them to open up. It's also great because we often disagree which helps keep the conversation going.
One last bit of advice. Put a time limit on your lessons. When I start with a new student I tell them we will learn together for six months. I've never had a student ask to stop before the six months and most want to continue after, but some students things jsit get repetitive with and I politely tell them my schedule has changed and I recommend someone else.