I am poor at English but I'm happy if I could help you a little. I felt that this question is a very difficult question. And I never thought of such a thing until now. This question is beneficial question even Japanese myself. I checked "昨" and "日" at Japanese site. I found that there is some pronunciation that is not display on dictionary. It's said "表外読み(Table outside readings)". and I found that "昨" have Table outside readings. It is きのう(yesterday). but 昨 alone does not mean "yesterday". 昨 have meaning "past day". We can't understand its meanings when it is only "昨". So, We add "日" or "年(year)" etc.. Then it will be "昨日(yesterday)" or "昨年(last year)" etc.. The above explanation is a case of Kun readings. Actually , we can read "昨日" without problem when case of On readings. When case of On readings, "昨" one of pronunciations is "さく" and "日" one of pronunciations is "じつ". We usually read "昨日" as "さくじつ" in the document. This word was also written on jisho.org. Did I help you? I am sorry if unclear points remain. Thank you very much.

I think jisho.org is the most useful online dictionary. It's the one I go to first. But you're right, it's not by any means complete or comprehensive. (Very surprised that it doesn't list the reading for 昨日). The other online resource I often use is honyakustar.com. It isn't much of a dictionary, and it doesn't list the on or kun readings. But if I'm trying to find the meaning of an obscure word, or am looking for sample sentences (and their English translations), it's very useful.

I've learned a lot from this thread. Thanks, Nagi! :)

きのう、きょう、あした are neither Kun readings nor On readings. They are some kind of irregular readings. And their Kanji expressions-昨日、今日、明日- are so-called "当て字(Ateji)". The readings of Ateji are not regarded as regular readings of their Kanji. So you cannot find the readings of Ateji on Kanji dictionary. But if you look up in hiragana -きのう、きょう、あす…-, you can find their Ateji easily./ Basically, Kanji are ideograms. So our ancestors have added the Japanese original readings (Kun readings) to Chinese original readings (On readings) . / But Kanji can be treated more freely. For example, The regular reading of 英国 is えいこく(On reading). But you can put Furigana to these Kanji as "イギリス、イングランド、ふるさと、ゆめのくに…" or anything you like. As far as the Kanji represents something you want to mean, you can pronounce the Kanji anyway. This is what we call Ateji. Of course, 英国 is not ふるさと for us. So you can never find such reading in dictionary. Ateji includes infinite reading styles./ Ateji have two different style. One uses Kanji's meaning (昨日=きのう). Another uses Kanji's sound (亜米利加=アメリカ). If you want to know more, please refer to Wikipedia.(https://en.m.wikipedia.org/wiki/Ateji)