That's a tough one. We've been quite fortunate in that department for the last few years as we've been growing by about 6-10 members a year. Mostly, our new members are mature adults. We've had a couple of teens but they don't seem to stay with it. I don't know if it's because they have other interests or just don't want to sit around with a bunch of ol' farts.
Throughout the year other organizations (schools, nature centers, state parks, etc.) ask us to provide demonstrations. We ask for volunteers and our members enjoy getting out to show and talk about our hobby. We don't charge anything but we do bring our printed brochure as a handout. The brouchure tells a little about the club, our community involvement, when and where we meet, and contact information. This always creates interest in our club.
We try to advertise our show and will shamelessly recruit interested attendees.
Meetings must be interesting. The business is a necessary evil but there needs to be more. We have a small raffle every month for some items; a book, palm gouge, tool bag, basswood, etc. We also have Show & Tell. Interest in that was declining until we started a raffle for participants. It doesn't cost anything but the only way to get a ticket is to bring a project to show and tell. We had 15-20 items on the table last night. Also, get input from the members about what they want at the meetings. You're not going to interest everyone at every meeting but you need to interest everyone at some point in time throughout the year.
Our club has a very large lending library for members. It includes magazines, books, study sticks, and videos. Members can checkout items for 2 months.
Each year we try to take a bus trip to a regional show. Many of our members wouldn't be comfortable driving a couple hours but are anxious to join the bus trip. We subsidize the trip for members from our treasurery and charge full price for non-members (including non-member spouses).
We take a couple months off in the summer but have a picnic in August. We try to include an interesting demo. One year we had a woodenshoe carver and another a chain-saw carver.
Wow, I just realized how busy we are! We've got a great group and we always try to express our appreciation for everything they do. Everyone likes the occasional

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Regards,
Jim