Kudos to McGrath of Harlow for "most of the "terrible rhymes", like the Lehrer ones, are actually perfect rhymes, just a bit unexpected."

None of the rhymes given as examples are really "terrible"; mostly just unexpected, near, slant, or deliberately (perversely) forced.

Why? English is probably one of the most rhyme-poor of languages, and so the tradition of near or complex rhymes has established itself.

If it's truly bad rhymes you want, in the sense of a tin ear or incompetence or impatience (in working out a good fit), then you could not do better (or is it worse?) than America's own Julia A. Moore, the Sweet Singer of Michigan (1847-1920). Whereas McGonigall's poems have a certain badness, he executes them with such great gusto and cheer. Mrs. Moore, on the other hand, became famous (or notorious) for her unending series of poems about dead infants and other morbid, "serious" topics.

You want a bad rhyme? Try Mrs. Moore's "Temperence Reform Clubs":
    Some enterprising people,
       In our cities and towns,
    Have gone to organizing clubs
       Of men that's fallen down.

Ogden Nash has acknowledged his debt to her; of her, as James Camp writes in Pegasus Descending:

few poets have so assiduously cultivated the line that rambles on for as long as necessary, nor produced more surpising rhymes. Given the first three lines of this quatrain, who could predict the way the fourth would end?
    Many a man joined a club
      That never drank a dram,
    These noble men were kind and brave,
      They do not care ------------.


...It goes, "They do not care for slang."
As the anonymous editor of a [reprint of one of her books]... has remarked, Mrs. Moore "not only conveys information, but she brings the mind up with a jerk. We look around quickly to see what made the noise, and feel instinctively for our money and our watch."

Doug