This diphthong may have appeared only in the Ossiriandic dialect. First, primitive [eu] became [eo] in Ossiriandic (PE19/25). Furthermore, it seems that [e] and [i] became [eo] before clusters of consonants beginning with [r] or [l], as with beorn < ᴹ✶ber(n)ō (Ety/BES) and meord < *mirdē < ᴹ✶mizdē (Ety/MIZD). This change is the same as the vowel-breaking process in the Old English language that inspired Ossiriandic, so it may have been limited to Ossiriandic as well.
According to the Comparative Tables, the diphthong [eo] later became [io] (PE19/25). This later diphthong does not appear in The Etymologies, while [eo] does, so perhaps the version of Ossiriandic described in The Etymologies was the earlier stage with [eo] and [ǣ].
Reference ✧ PE19/25 ✧ eo
||✧ PE19/25 (†eu > eo)|
||✧ PE19/25 (eo > io)|