Probably the biggest category of uncatalogued modern (post 1991 cards) Japanese baseball cards are those that are issued either by the NPB teams themselves or their official fan clubs. I think the latest edition of Engel that dealt with modern cards only listed a couple sets and that's over six years out of date now. Jason did a post from a few years ago listing all the cards from all the sets that he has located (and he's still updating this post as he learns about new stuff) which is probably the most comprehensive listing of these cards that exists in the English speaking blogosphere. I don't intend to change that, but I did think that I'd start doing some posts on some of the team sets (OK, cards from team sets) that I've been picking up lately and provide a complement to Jason's post.
I'm going to start with some cards I've gotten from the Swallows because these turned out to be kind of confusing and they serve as a warning to how deep this rabbit hole might be...
The first set I have representation from is the 2008 "Premium Card" set. I only have two cards from this set - Shun Takaichi (#Ys07) and Ryuji Miyade (#Ys39):
Next up is a second "Premium Card" set from 2008. This one is labeled "Vol. 2". I have three cards from this set - Ryo Kawashima (#Ys05), Atsushi Kinugawa (#Ys19) and Yasushi Iihara (#Ys29):
This set has a "kira" parallel (that may not be clear from the scan):
I thought initially that there was also a "red facsimile autograph" parallel for this set as well, but when I looked closely I realized that these cards were actually from another set - a "Printing Autograph Premium Card Vol. 2" set. I have three cards from this set as well - Shigeru Takada (#YsS01), Masanori Ishikawa (#YsS04) and Tatsuyoshi Masubuchi (#YsS05).
The Swallows did something similar for 2009. I have one card from a "plain" team set and two cards from a similar looking set with a red facsimile autograph. I'm not sure what (if any) name the set has.
My card from the "plain" set is Yasushi Iihara (#Ys37):
My facsimile autograph set cards are Ryohei Kawamoto (#YsS08) and Kazuhiro Hatakeyama (#YsS12):
I have a couple cards from another 2009 set. These are clear plastic cards similar to the 2001 BBM Golden Glove cards. They are essentially one-sided as the backs of the card simply show the reverse of the image on the front. I have three of these - Shinya Miyamoto (#YsC06), Hiroyasu Tanaka (#YsC07) and Kazuki Fukuchi (#YsC08):
The next cards I have are from 2011 and again there are two similarly looking sets - one with no autographs and one with autographs. Again there is no indication on the cards what the name of the set is.
I only have two cards from the "plain" set - Katsuki Dobashi (#Ys03) and Aaron Guiel (#Ys41):
I have seven from the facsimile autograph set - Kyohei Muranaka (#YsS06), Tatsuyoshi Masubuchi (#YsS08), Shohei Tateyama (#YsS09), Yuki Shichijyo (#YsS10), Atsushi Fujimoto (#YsS15), Kazuhiro Hatakeyama (#YsS17) and Shingo Kawabata (#YsS18):
I have six cards from another 2011 set that has a "kira" finish on the front - Kyohei Muranaka (#YsK03), Masanori Ishikawa (#YsK04), Shohei Tateyama (#YsK05), Hiroyasu Tanaka (#YsK08), Osamu Hamanaka (#YsK09) and Norichika Aoki (#YsK10):
Finally I have three cards from a similar "kira" set from 2012 - Shohei Tateyama (#YsK05), Katsuki Akagawa (#YsK06) and Tsuyoshi Ueda (#YsK10):
The only cards listed here that explicitly list the year they came out are the 2008 cards. The cards I think are from 2009 have the "Yakult 40th Anniverary" logo on them which is why I figure they are from 2009. I'm going by what the seller of the cards said for the 2011 and 2012 cards so it's possible that those are not correct.
I don't know how these cards are distributed - if it is by pack then it wouldn't surprise me to discover that the facsimile autograph cards as well as the "clear" and "kira" cards are insert sets associated with a base team set.