Etymonline to the rescue:
1650s, “table of contents of a series of lectures, etc.,” from Late Latin syllabus “list,” ultimately a misreading of Greek sittybos “parchment label, table of contents,” of unknown origin. The misprint appeared in a 15c. edition of Cicero’s Ad Atticum (see OED). Had it been a real word, the proper plural would be syllabi.
The full OED entry for the word mentioned by Etymonline is much too long to fully cite here, but includes the following material pertinent to the current discussion:
Etymology
< modern Latin syllabus, usually referred to an alleged Greek
σύλλαβος. Syllabus appears to be founded on a corrupt reading syllabos
in some early printed editions — the Medicean MS. has sillabos — of
Cicero Epp. ad Atticum ɪ. iv, where the reading indicated as correct by
comparison with the MS. readings in ɪ. v. and viii. is sittybas or Greek
σιττύβας, accusative plural of sittyba, σιττύβα parchment label or
title-slip on a book. (Compare Tyrrell and Purser Correspondence of Cicero
nos. 107, 108, 112, Comm. and Adnot. Crit.) Syllabos was græcized by
later editors as συλλάβους, from which a spurious σύλλαβος was deduced
and treated as a derivative of συλλαμβάνειν to put together, collect
(compare ꜱʏʟʟᴀʙʟᴇ n.).
In the passage from S. Augustine’s Confessions xɪɪɪ. xv. (‘ibi legunt
[sc. angeli] sine syllabis temporum quid velit aeterna voluntas tua’)
commonly adduced as further evidence of Latin syllabus, the word is clearly
syllaba syllable.
The earliest provided citation dates from a 1656 work by antiquary and
lexicographer Thomas Blount in his Glossographia; or, A dictionary
interpreting all such hard words, whether Hebrew, Greek or Latin... as are
now used in our refined English tongue (1ˢᵗ edition, 1656, London), where
he writes:
- Syllabus, a Table or Index in a Book, to shew places or matter by
Letters or Figures.
This was quickly followed in 1667 by Jeremy Taylor, Church of Ireland
Bishop of Down and Connor, in the 4ᵗʰ edition of his work The
great exemplar of sanctity and holy life (1ˢᵗ edition 1649, 4ᵗʰ edition 1667), where he writes at ɪ. vi. §22. 160:
- The Apostle expresses it still by Synonyma’s, Tasting of the heavenly
gift, and made partakers of the holy Ghost..; all which also are a
syllabus or collection of the several effects of the graces bestowed in
Baptism.
So, it seems that it is based on a misspelling of a Greek word — but that would hardly give one reason to form the plural in Greek starting from the Latin(ized) form.
According to both Merriam-Webster and the OED alike, the plural can be either syllabi /ˈsɪləbaɪ/ or syllabuses /ˈsɪləbəsɪz/, but with Etymonline’s “no real word” verdict, I’d go for the latter.