ko (from older *kə) is native Japonic ancient proximal demonstrative pronoun ("this"), now surviving as prefix. Rarely used kanji spelling for this prefix is 此.
Some words with this prefix:
kore ([此]{こ}れ) "this"
kono ([此]{こ}の) "this"
konna ([此様]{こん}な) "this kind", contraction of [此]{こ}の[様]{よう}な
koko ([此処]{ここ}) "this place"
kotabi ([此]{こ}[度]{たび}) "this time"
kotosi ([今年]{ことし}) "this year"
kyō ([今日]{きょう}) "this day"
Word meaning "this day" developed in this way:
*/kʲe/ + */pu/ → */kʲepu/ → /kepu/ → /keu/ → /kʲoː/
*/kʲe/ was apophonic form of */kə/ "this".
*/pu/ was apophonic form of */pi/ "day".
kesa ([今朝]{けさ}) "this morning"
Word meaning "this morning" developed in this way:
*/kʲe/ + */asa/ → */kʲesa/ → /kesa/
*/kʲe/ was apophonic form of */kə/ "this".
When 2 consecutive vowels would occur in one word (in this case */ʲea/), in most cases, vowels would fuse or one vowel would be elided (here initial */a/ from */asa/).
koyoi ([今宵]{こよい}) "this evening"
(Phonological developments and phonemic realizations according to Frellesvig (2010))
Usage of kanji 今 "now" instead of kanji 此 "this" for words 今年, 今日, 今朝 and 今宵 are examples of [熟]{じゅく}[字]{じ}[訓]{くん}, i.e. kanji used for meaning but not reading.
今年, 今日 and 今朝 also have regular Sino-Japanese on'yomi readings, こんねん, こんにち and こんちょう.
Kanji 今 has only on'yomi こん and きん and kun'yomi いま, so there is no reason for any kyōnen (きょうねん) reading of word 今年.
There happens to exist similarly sounding word kyonen ([去]{きょ}[年]{ねん}, with short /o/), which means "last year".
Some more information about *kə in Old Japanese:
Alexander Vovin (2020, "A Descriptive and Comparative Grammar of Western Old Japanese", "Chapter 4 Nominals, Section 2.4.1.1.1.1 Isolated Form kǝ", pages 263-264):
2.4.1.1.1.1 Isolated Form kǝ
Isolated form kǝ is attested in Western Old Japanese in three examples in the Kojiki kayō with the following particles, and once in the Nihonshoki kayō, modifying the following noun yǝpi ‘night.’ Both usages survived into Classical Japanese, but there they become even more infrequent. In modern Japanese this isolated form survived only in compounds like kotosi ‘this year’ (OJ kǝ tǝsi).
許母布佐波受
kǝ mǝ pusap-anz-u
this FP be suitable-NEG-FIN
This is not suitable, either (KK 4)
許斯與呂志
kǝ si yǝrǝsi
this EP be good
this is good (KK 4)
許斯母阿夜爾加志古志
kǝ si mǝ aya n-i kasiko-si
this EP FP very DV-CONV be awesome-FIN
This is very awesome, too (KK 100)
区茂能於虚奈比虚予比辞流辞毛
kumo-nǝ okǝnap-i kǝ yǝpi siru-si mo
spider-GEN perform-NML this night be distinctive-FIN EP
the spider’s performance is distinctive tonight (NK 65)
In this example kǝ has a modifier function without the following n-ǝ.