The World God Only Knows (aka Kami nomi zo Shiru Sekai aka Kaminomi) has had some unusual merchandising before as they have previously released everything from puzzles featuring the characters to The World Bread Only Knows to a compact mirror with Elsie's picture.
Now Amazon.jp has started taking pre-orders for volume 13 of the manga, which is due out on 6/28. For 950 yen, 510 yen more than the regular edition, the special edition is listed as coming with a digital clock. Although a picture has not been released, it seems likely that it will include some image of the characters on it to tie it in.
Previously, the special edition of volume 10 of the manga included a DVD, volume 11 included a calendar, and volume 12 (pictured above) included a stainless steel bookmark with Haqua and Elsie's picture.
Image ©Tamiki Wakaki / Shogakukan, Otoshigami Kaketama Tai, TV Tokyo