Like the title states I have found a kanji character which I believe lacks an Onyomi reading. It's this one "喰". According to google search results here's a page which has missing Onyomi reading: http://jigen.net/kanji/21936
The reason I noticed this now is because I was reading a novel in Japanese and a word there had this kanji in it but it didn't make sense to use the Kunyomi version there so here we are.
Hmm, perhaps those two sites do not have everything? Just saying. Also, the moment I fist saw that kanji I instantly thought that it's onyomi reading should be "しょく" Similar to this "食".
I see. Well, it might have been the novel author's self-created word, but it is true that it didn't make any sense to read that word using the Kunyomi readings.