20 years ago, my club didn't have a "reasonable" junior golf membership program, and the aging population definately reflected it. We surveyed other clubs in the area, and came up with a program that really revitalized the club. (All juniors get the same break; no special deal for legacies, other than making it easier to get in!). I forget the details, but under a certain age one is exempt from initiation (with a three year pro-ration as one nears the cutoff for regular membership). There is also a break on dues, and a cap on the number of junior members.
I believe that we went from 1 junior member before these changes, to a waiting list, in a very short time.
Though there has been some problem with people dropping out when the dues bump up, many of the junior members stay on, and are active users of all the club facilities (often playing 36 a day), which helps keep a strong caddy program, and fully-utilized kitchen.