Just joined the forum, and fairly new at silhouette myself. Seeing as no one answered your questions yet, I'll put in my $0.02:
Have a "fun match" every so often, say once or twice a year. Advertise it in your local paper, making sure to have directions and a contact name/phone number.
A lot of people (like me) are intimidated by the idea of going out and shooting first time in a competition, especially if they don't know much about the sport. A fun match gives folks a way of getting introduced to the sport without feeling pressured to perform well. And how many of us DID perform well first match out?
Have something for the kids as well. It's easy enough to make up cardboard cut-outs of the targets and set them close enough so the kids can have a good time with a BB gun. Kids who want to shoot will bring along parents who just might decide it looks like fun, too. Plus, hook the kids and you now have new members literally growing into the sport.
Get some of your NRA instructor members to do a Boy Scout/Girl Scout Merit Badge course. Boy Scouts has a rifle merit badge, and although shooting silhouette isn't part of it, you could always tag on some .22 rifle silhouette as a fun activity to go along with the course itself. Trust me, rifle merit badge is so popular that when I would take my troop to summer camp we'd have a hard time getting everyone who wanted to take the course into it - just not enough guns nor instructors for all the boys. For youngsters, shooting at paper targets is, well, okay. But if it flies or falls down when you shoot it they go ape over it! We used to practically have to pry the firearms out of the kids' hands when they were doing Rifle, Shotgun, or Black Powder merit badges.
Get someone who can take pictures and write as well. Do up a nice article for your paper - they eat stuff involving kids up and would in all likelihood print an article you just hand to them. Invite local television, too, if you have a good contact. If it's a good story, lots of action, smiling happy kids it will also likely get aired. The activity is incidental to what you do, but will advertise your club nonetheless.
Ask places that sell ammo to let you post fliers. Even better, have a stack of them that people can take. Advertise dates of meets, contact names and phone numbers, etc. Put a map to your club on the back. Most places are happy to do it, knowing that the more shooting events people get involved in the more business they will do in their shop. (People who shoot invariably need STUFF.) Plus, if you're already a customer the shop owner will want to keep you happy, and might see your recruiting efforts as a good way of getting more customers.
There are lots of inexpensive ways to get the word out. In my area, there are 4 clubs within 50 miles of each other, all shooting silhouette. At least two of the four shoot every Sunday. Just got back from a match at a club that can shoot 2 long range and three small bore banks at a time, and they had to run 2 relays on the long range and three on the small bore. (Do the math - that's 5-8 on the long range, and 9-12 on the small bore range, or between 14 and 20 participants.) And the other club that shoots every Sunday has as many banks as this club and also typically runs two or three relays. How did I get involved? A fun match caught my eye, and I've been hooked ever since!