“What IS daf yoineh?” you might ask. As a child, I used to hear people, usually of the Satmar domination, call Daf yomi that. People with a heavy Hungarian Hasidic accent tend to pronounce words that end with a chirik, with a shva. For example, the word כללי (as in תיקון כללי or שיעור כללי) is pronounced as kluleh, and יומי is pronounced as Yoimeh. At one point, someone thought it’ll be funny to call it Daf Hayoineh instead of Daf Hayoimeh, and the name stuck.
So who was that someone? In the recently published “Ginat Veradim” (vol. 15 5772), a quarterly published by the Zaalonite Satmar fraction, a collection of stories “on the subject of our rabbis’ opposition to Daf Yomi” was featured, in honor of the upcoming Siyum Hashas. Here’s one gem:
סיפר הרב הגאון המפורסם מוה"ר משה ארי' לעוו ז"ל הרב מטעמעשוואר שהרה"ק מנאסויד הי' מזלזל בדף היומי, והיה קוראו בלשון גנאי "דף היונה"...
(מפי נכדו הרב אא"ד הי"ו שממעו ממנו)
The rav of Timișoara, R. Moshe Aryeh Lev related that the holy Rabbi [Abraham Joshua Freund] of Năsăud used to disparage the daf yomi, and he used to call it in a derogatory way “daf hayoineh”…
I don't know if this is true or not, but if it is, then this might be the origin of the term, or at least one of the origins.
But I was surprised to see the following letter in Hamodia’s weekly magazine “Inyan” (Vol. XV, issue 715 p. 4):
A short while ago you printed a letter (Parshas Shelach/June 13) claiming that Harav Meir Shapiro’s status as the originator of Daf Yomi was in question and stating that “there are many proofs for it”. I would like to make the following points. …. [T]here is a well-known story (cited in at least one place in Aleinu L’shabei’ach, Shemos, p. 548) that after Harav Shapiro became famous, he met someone from his hometown and asked if the other person remembered that they had played together as children. When the man replied in the affirmative, he asked, “Do you remember that I used to dream of initiating a program of Shas for all of Klal Yisrael, and the children used to laugh at me calling it ‘daf hayoneh’?” The man said he remembered that too. Rav Shapiro responded, “I’m telling you this because it is important to remember never to laugh at the dreams of a child!”
In addition to the obvious lesson in this story, it seems clear that he was already thinking of the idea when he was very young. ….
It would seem from this letter that the derogatory term was born together with the idea of Daf Yomi itself. Alas, to my non-surprise, looking up the story in Aleinu Leshabe’ach I found that he tells the story all right but without the part about the children calling it daf hayoneh. That part is most obviously an anachronism added by Mr. Klein. Not that I would trust Aleinu Leshabe’ach's version of the story any more than I trust Mr. Leibel Klein, considering the outrageous stories the book is fond of telling kayadua, but the fact that Aleinu Leshabeach records the legend without the part about daf hayoneh is definitely telling.
Speaking of the originator of the Daf Yomi idea, let me just point you in the direction of S.’ post on the matter here. It is interesting to not though, that what S. cites was already mentioned in an article in Yeshurun by R. Eliezer Katzman who thanks Prof. Shneur Zalman Lehman for pointing it out.