Why was Tokyo sometimes called “Tokiyo”?
The Japanese hiragana for Tokyo is とうきょう, and according to Wikipedia’s article on the romanisation of Japanese, the “きょ” component would be romanised, under all of the Hepburn, Nihon-shiki, and Kunrei-shiki systems as “kyo”.
The section on historical romanisations has “kio” as a romanisation of “きょ”, but that was a romanisation suggested in the 1600s. Were those romanisation schemes still in use in the 19th century, for a city renamed in 1868?
The name Tokyo is represented by two characters in Japanese: 東京 and the syllables (some fussy linguists insist those be called morae) used to sound those out are four: とうきょう or to-u-k[yo]-u. Japanese is an isochronous language, meaning every syllable has to be expressed as a (roughly equivalent) duration in time; whatever you call that duration, Tokyo has four beats in Japanese but three in English.
Note that the third syllable, which normally represents the sound ki, has a tiny subscript yo next to it. This is how the Japanese introduce what is essentially a y-glide between the consonant and vowel sounds of certain syllables, because no single character in the syllabary can be used to express those sounds without creating another syllable.
I just asked my wife’s aunt, who is Japanese and taught Japanese to college students, about the oddball spelling you point out. She explains that some renderings of Tokyo were given as Tokiyo as a way of bringing the ょ across in the transliteration. This is non-standard, however, and should be avoided, since most English readers hardly care about the phonological representation of such an abstruse issue as this.
Additional note: The u sounds in the original Japanese, coming at the end of rounded vowels, are almost completely disregarded by Western ears. Syllable duration isn’t encoded for meaning to our ears, so those u sounds get dropped when a Westerner makes a transliteration. What remains from Tokyo, then, is to-ki-yo, which is how it’s pronounced in English. The “tokiyo” spelling, then, seems to represent rather an obdurate insistence that the pronunciation be entirely Anglicized for English consumption.
Further elucidation: I believe the way to think about Japanese “syllables” is to liken them to music on a phonograph that may be sped up or slowed down. The speed of the passing notes may change, but their relationship to each other at any given speed remains the same. You may hear a Japanese speaker rush through part of a sentence but the syllables will all be there relative to each other at any given speed.