The first independent minor league in Japan was the Shikoku Island League, which started play in 2005. It was founded by former Seibu Lion Hiromichi Ishige. Shikoku is the only one of the four major islands of Japan that has no NPB team. The four teams in the league (the Ehime Mandarin Pirates, the Kagawa Olive Guyners, the Kochi Fighting Dogs and the Tokushima Indigo Socks) each call one of the four prefectures of Shikoku home.
Naturally the first thing I wondered when I heard there was an independent league in Japan was whether or not they had baseball cards. The answer turns out to be "yes, at least in 2006 and 2007". I had seen some of these cards on Yahoo! Japan Auctions but I only recently picked up a couple of the 2006 cards from Ebay:
Here's what the back of one of the cards looks like:
I suspect but I don't know for sure that the cards were given away individually to ticket holders when they entered the park, kind of the same way Ryan described the JWBL cards being distributed. So I don't think the cards are available as team sets and putting a set together is probably very difficult.
I did a little research on these five particular players and as far as I can tell, none of them were ever the property of an NPB team. I was surprised to discover that the one Indigo Sock player I have, Taichi Komatsuzaki, is now a professional cyclist.
I have seen cards on Yahoo! Japan Auctions from both 2006 and 2007 but I don't know if there are any from any other years. Katsuya Kakunaka of the Marines, arguably the biggest export from the league, has a Kochi Fighting Dogs card from 2006, one of the rare instances of a "pre-rookie" card in Japan. (I don't have this card - I swiped the image off of YJA).
There are three cards for the league that were issued by Sports Card Magazine - two of them in the September 2005 issue and one (for Hideki Irabu when he joined the Kochi Fighting Dogs) in the September 2009 issue.
UPDATE: Ryan said there were team sets for sale on the team websites, something I should have thought of. There are listings for the 2006 team sets for Ehime and Kochi, the 2007 team sets for Ehime, Kagawa, Kochi and Tokushima and Kochi team sets from 2013 and 2014. I've linked to everything that I could find in the team & league shops but some of the items are out of stock.