History of pronunciation of "moiety"
Wiktionary shows the pronunciation of moiety as /ˈmɔɪ.ə.ti/, which I think agrees with the audio versions at merriam-webster.com and howjsay.com. (Be warned that both those links produce audio when clicked.) Anyhow, from an 1832-vintage quotation for sense 1 at wiktionary (meaning half), I have the impression that at some times or places the word has been pronounced with 4 syllables instead of 3, and rhyming with society:
From New Holland the emu,
With his better moiety,
Has paid a visit to the Zoological Society.
Has its pronunciation changed since then? Or was this perhaps meant to be merely a half rhyme?
Edit: A half rhyme, or near rhyme, or imperfect rhyme, entails consonance on the final consonants of the words involved. Moiety (/ˈmɔɪ.ə.ti/) and society (/s@"[email protected]/) rise a little above that level, but not to the level of perfect rhyme, which according to wikipedia's rhyme article, entails having final stressed vowel and all following sounds identical. But /ɔɪ/ and /aI/ are not identical.
Solution 1:
If the poet spoke a dialect with the loin-line merger, this would have been an exact rhyme. That is, the 'oi' diphthong in "moiety" would have been pronounced the same as the 'i' in "society". According to the linked webpage, this occurs in some dialects in Southern England, and may have been more widespread when the poem was written.
This book says that for some words, the loin/line merger was widespread in England in the last half of the 18th century, but "by the end of the century the merger was in retreat, if still acceptable; by the next century spellings like bile, jine were provincial stereotypes". So it's possible that a three-syllable moiety would have been an exact rhyme for society not that long before this poem was written. If this merger was widespread enough, or recent enough, that people were used to hearing it, the rhyme would have been reasonable even if the poet didn't use that pronunciation.
EDIT: The pronunciation of the diphthong "i" (now /aɪ/) changed during the Great Vowel Shift, and when it passed "oi" (now /ɔɪ/) during the 18th century, these two diphthongs were close enough that they were merged in the speech of much of the population, and made very good near-rhymes for most of the rest. So rather than moiety being pronounced with an /aɪ/, it would have been society that was pronounced like sosoyety.
Solution 2:
In the 19th century, I would expect the "i" to have been printed with a diaeresis (moïety) if it were not part of the oi diphthong.
I see no reason to doubt that this was a poetic device.